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[1]
A. P. Calderón :
“Integrales singulares y operadores seudodiferenciales: Historia y perspectiva ”
[Singular integrals and pseudodifferential operators: History and perspective ],
Anales Acad. Nac. Ciencias Exac. Fís. y Nat.
38 ,
pp. 33–45 .
article
BibTeX
@article {key92995502,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Integrales singulares y operadores seudodiferenciales:
{H}istoria y perspectiva [Singular integrals
and pseudodifferential operators: {H}istory
and perspective]},
JOURNAL = {Anales Acad. Nac. Ciencias Exac. F\'{\i}s.
y Nat.},
FJOURNAL = {Anales de la Academia Nacional de Cienceas
Exacta, F\'{\i}sicas y Naturales},
VOLUME = {38},
PAGES = {33--45},
ISSN = {0365-1185},
}
[2]
A. P. Caldéron, A. González Domínguez, and A. Zygmund :
“Nota sobre los valores límites de funciones analíticas Note on the limit values of analytic functions ],
Revista Unión Mat. Argentina
14
(1949 ),
pp. 16–19 .
MR
0031550 Zbl
0033.05901 article
People
BibTeX
@article {key0031550m,
AUTHOR = {Cald\'eron, A. P. and Gonz\'alez Dom\'{\i}nguez,
A. and Zygmund, A.},
TITLE = {Nota sobre los valores l\'{\i}mites
de funciones anal\'{\i}ticas [Note on
the limit values of analytic functions]},
JOURNAL = {Revista Uni\'on Mat. Argentina},
FJOURNAL = {Revista de la Uni\'on Matem\'atica Argentina},
VOLUME = {14},
YEAR = {1949},
PAGES = {16--19},
URL = {http://inmabb.criba.edu.ar/revuma/pdf/v14n1/p016-019.pdf},
NOTE = {MR:0031550. Zbl:0033.05901.},
ISSN = {0041-6932},
}
[3]
A. P. Calderón and A. Zygmund :
“Note on the boundary values of functions of several complex variables ,”
pp. 145–165
in
A. Zygmund, W. Transue, M. Morse, A. P. Calderón, and S. Bochner :
Contributions to Fourier analysis .
Annals of Mathematics Studies 25 .
Princeton University Press (Princeton, NJ ),
1950 .
MR
0035833 Zbl
0040.04001 incollection
People
BibTeX
@incollection {key0035833m,
AUTHOR = {Calder\'on, A. P. and Zygmund, A.},
TITLE = {Note on the boundary values of functions
of several complex variables},
BOOKTITLE = {Contributions to {F}ourier analysis},
SERIES = {Annals of Mathematics Studies},
NUMBER = {25},
PUBLISHER = {Princeton University Press},
ADDRESS = {Princeton, NJ},
YEAR = {1950},
PAGES = {145--165},
NOTE = {MR:0035833. Zbl:0040.04001.},
ISSN = {0066-2313},
}
[4]
A. P. Caldéron :
I: On the ergodic theorems; II: On the behavior of harmonic functions at the boundary; III: On the theorem of Marcinkiewicz and Zygmund Ph.D. thesis ,
University of Chicago ,
1950 .
Advised by A. Zygmund .
Part II had earlier been published in Trans. Am. Math. Soc. 68 :1 (1950)Trans. Am. Math. Soc. 68 :1 (1950)
MR
2611391 phdthesis
People
BibTeX
@phdthesis {key2611391m,
AUTHOR = {Cald\'eron, A. P.},
TITLE = {I: {O}n the ergodic theorems; {II}:
{O}n the behavior of harmonic functions
at the boundary; {III}: {O}n the theorem
of {M}arcinkiewicz and {Z}ygmund},
SCHOOL = {University of Chicago},
YEAR = {1950},
URL = {http://search.proquest.com/docview/301805666},
NOTE = {Advised by A. Zygmund. Part
II had earlier been published in \textit{Trans.
Am. Math. Soc.} \textbf{68}:1 (1950).
Part III had also earlier been published
in \textit{Trans. Am. Math. Soc.} \textbf{68}:1
(1950). MR:2611391.},
}
[5]
A. P. Calderón :
“On a theorem of Marcinkiewicz and Zygmund Trans. Am. Math. Soc.
68 : 1
(January 1950 ),
pp. 55–61 .
This was one of three published articles combined to make up the author’s 1950 PhD thesis .
MR
0032864 Zbl
0035.18903 article
Abstract
BibTeX
The purpose of the present paper is to prove the following result:
Let \( F(P) \) , \( P=(x_1,x_2,\dots,x_n) \) , be a function harmonic for \( x_n > 0 \) and such that for every point \( Q \) of a set \( E \) of positive measure on the hyperplane \( x_n=0 \) there exists a region contained in \( x_n > 0 \) limited by a cone with vertex at \( Q \) and a hyperplane \( x_n = 0 \) there exists a region contained in \( x_n > 0 \) limited by a cone with vertex at \( Q \) and a hyperplane \( x_n = \) const. where the function is bounded. Then except for a set of measure zero, the integral
\[ \int \frac{1}{x_n^{n-2}}\operatorname{grad}^2F \,d\omega, \]
extended over any region limited by a cone with vertex at \( Q \in E \) , a hyperplane \( x_n = \) const., and contained in \( x_n > 0 \) , is finite.
@article {key0032864m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {On a theorem of {M}arcinkiewicz and
{Z}ygmund},
JOURNAL = {Trans. Am. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {68},
NUMBER = {1},
MONTH = {January},
YEAR = {1950},
PAGES = {55--61},
DOI = {10.2307/1990538},
NOTE = {This was one of three published articles
combined to make up the author's 1950
PhD thesis. MR:0032864. Zbl:0035.18903.},
ISSN = {0002-9947},
}
[6]
A. P. Calderón :
“On theorems of M. Riesz and Zygmund Proc. Am. Math. Soc.
1 : 4
(August 1950 ),
pp. 533–535 .
MR
0037394 Zbl
0040.32302 article
BibTeX
@article {key0037394m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {On theorems of {M}. {R}iesz and {Z}ygmund},
JOURNAL = {Proc. Am. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical
Society},
VOLUME = {1},
NUMBER = {4},
MONTH = {August},
YEAR = {1950},
PAGES = {533--535},
DOI = {10.2307/2032325},
NOTE = {MR:0037394. Zbl:0040.32302.},
ISSN = {0002-9939},
}
[7]
A. P. Calderón :
“On the behaviour of harmonic functions at the boundary Trans. Am. Math. Soc.
68 : 1
(January 1950 ),
pp. 47–54 .
This was one of three published articles combined to make up the author’s 1950 PhD thesis .
MR
0032863 Zbl
0035.18901 article
BibTeX
@article {key0032863m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {On the behaviour of harmonic functions
at the boundary},
JOURNAL = {Trans. Am. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {68},
NUMBER = {1},
MONTH = {January},
YEAR = {1950},
PAGES = {47--54},
DOI = {10.2307/1990537},
NOTE = {This was one of three published articles
combined to make up the author's 1950
PhD thesis. MR:0032863. Zbl:0035.18901.},
ISSN = {0002-9947},
}
[8]
A. P. Calderón and A. Zygmund :
“On the theorem of Hausdorff–Young and its extensions ,”
pp. 166–188
in
A. Zygmund, W. Transue, M. Morse, A. P. Calderón, and S. Bochner :
Contributions to Fourier analysis .
Annals of Mathematics Studies 25 .
Princeton University Press ,
1950 .
MR
0037395 Zbl
0040.02902 incollection
People
BibTeX
@incollection {key0037395m,
AUTHOR = {Calder\'on, A. P. and Zygmund, A.},
TITLE = {On the theorem of {H}ausdorff--{Y}oung
and its extensions},
BOOKTITLE = {Contributions to {F}ourier analysis},
SERIES = {Annals of Mathematics Studies},
NUMBER = {25},
PUBLISHER = {Princeton University Press},
YEAR = {1950},
PAGES = {166--188},
NOTE = {MR:0037395. Zbl:0040.02902.},
ISSN = {0066-2313},
}
[9]
A. P. Calderón :
“On the differentiability of absolutely continuous functions ,”
Rivista Mat. Univ. Parma
2
(1951 ),
pp. 203–213 .
MR
0045200 Zbl
0044.27901 article
BibTeX
@article {key0045200m,
AUTHOR = {Calder\'on, Alberto P.},
TITLE = {On the differentiability of absolutely
continuous functions},
JOURNAL = {Rivista Mat. Univ. Parma},
FJOURNAL = {Rivista di Matematica della Universit\`a
di Parma. Serie IV},
VOLUME = {2},
YEAR = {1951},
PAGES = {203--213},
NOTE = {MR:0045200. Zbl:0044.27901.},
ISSN = {0035-6298},
}
[10]
A. P. Calderón and A. Zygmund :
“A note on the interpolation of linear operations Studia Math.
12
(1951 ),
pp. 194–204 .
MR
0046567 Zbl
0044.11902 article
Abstract
People
BibTeX
@article {key0046567m,
AUTHOR = {Calder\'on, A. P. and Zygmund, A.},
TITLE = {A note on the interpolation of linear
operations},
JOURNAL = {Studia Math.},
FJOURNAL = {Studia Mathematica. Polska Akademia
Nauk},
VOLUME = {12},
YEAR = {1951},
PAGES = {194--204},
DOI = {10.1007/978-94-009-1045-4_1},
NOTE = {MR:0046567. Zbl:0044.11902.},
ISSN = {0039-3223},
}
[11]
A. P. Calderon and G. Klein :
“On an extremum problem concerning trigonometrical polynomials Studia Math.
12 : 1
(1951 ),
pp. 166–169 .
MR
0050043 Zbl
0044.05902 article
People
BibTeX
@article {key0050043m,
AUTHOR = {Calderon, A. P. and Klein, G.},
TITLE = {On an extremum problem concerning trigonometrical
polynomials},
JOURNAL = {Studia Math.},
FJOURNAL = {Studia Mathematica. Polska Akademia
Nauk. Instytut Matematyczny},
VOLUME = {12},
NUMBER = {1},
YEAR = {1951},
PAGES = {166--169},
URL = {http://matwbn.icm.edu.pl/ksiazki/sm/sm12/sm12119.pdf},
NOTE = {MR:0050043. Zbl:0044.05902.},
ISSN = {0039-3223},
}
[12]
A. P. Calderon and A. Zygmund :
“On the existence of certain singular integrals Acta Math.
88
(December 1952 ),
pp. 85–139 .
Dedicated to Professor Marcel Riesz, on the occasion of his 65th birthday.
MR
0052553 Zbl
0047.10201 article
People
BibTeX
@article {key0052553m,
AUTHOR = {Calderon, A. P. and Zygmund, A.},
TITLE = {On the existence of certain singular
integrals},
JOURNAL = {Acta Math.},
FJOURNAL = {Acta Mathematica},
VOLUME = {88},
MONTH = {December},
YEAR = {1952},
PAGES = {85--139},
DOI = {10.1007/BF02392130},
NOTE = {Dedicated to Professor Marcel Riesz,
on the occasion of his 65th birthday.
MR:0052553. Zbl:0047.10201.},
ISSN = {0001-5962},
}
[13]
A. P. Calderón and R. Pepinsky :
“On the phases of Fourier coefficients of positive real periodic functions ,”
pp. 339–349
in
Computing methods and the phase problem in X-ray crystal analysis
(State College, PA, 6–8 April 1950 ).
Edited by R. Pepinsky .
Pennsylvania State College Department of Physics ,
1952 .
incollection
People
BibTeX
@incollection {key28684479,
AUTHOR = {Calder\'on, A. P. and Pepinsky, R.},
TITLE = {On the phases of {F}ourier coefficients
of positive real periodic functions},
BOOKTITLE = {Computing methods and the phase problem
in {X}-ray crystal analysis},
EDITOR = {Pepinsky, Ray},
PUBLISHER = {Pennsylvania State College Department
of Physics},
YEAR = {1952},
PAGES = {339--349},
NOTE = {(State College, PA, 6--8 April 1950).},
}
[14]
A. P. Calderon and H. B. Mann :
“On the moments of stochastic integrals Sankhyā
12 : 4
(September 1953 ),
pp. 347–350 .
MR
0057954 Zbl
0051.10402 article
Abstract
People
BibTeX
Let \( y_n = (x_n^{(1)},\dots,x_n^{(k)}) \) be a sequence of random vectors, converging in measure to a random vector \( y = (x^{(1)},\dots \) , \( x^{(k)}) \) . In this paper we shall find necessary and sufficient conditions that the joint moments of \( x_n^{(1)},\dots \) , \( x_n^{(k)} \) converge to the corresponding moments of \( x^{(1)},\dots \) , \( x^{(k)} \) . Our results will be applied to compute the joint moments of stochastic integrals when the joint moments of the integrands are given.
@article {key0057954m,
AUTHOR = {Calderon, A. P. and Mann, H. B.},
TITLE = {On the moments of stochastic integrals},
JOURNAL = {Sankhy\=a},
FJOURNAL = {Sankhy\=a. The Indian Journal of Statistics},
VOLUME = {12},
NUMBER = {4},
MONTH = {September},
YEAR = {1953},
PAGES = {347--350},
URL = {http://www.jstor.org/stable/25048145},
NOTE = {MR:0057954. Zbl:0051.10402.},
ISSN = {0972-7671},
}
[15]
A. P. Calderón :
Solution of the scalar radiation problem for surfaces of revolution .
Technical report A. F. 18 (600) 88, 478-17 ,
Antenna Laboratory, Ohio State University Research Foundation ,
1953 .
techreport
BibTeX
@techreport {key89446316,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Solution of the scalar radiation problem
for surfaces of revolution},
NUMBER = {A. F. 18 (600) 88, 478-17},
INSTITUTION = {Antenna Laboratory, Ohio State University
Research Foundation},
YEAR = {1953},
PAGES = {4},
}
[16]
A. P. Calderon :
“A general ergodic theorem Ann. Math. (2)
58 : 1
(July 1953 ),
pp. 182–191 .
MR
0055415 Zbl
0052.11903 article
BibTeX
@article {key0055415m,
AUTHOR = {Calderon, A. P.},
TITLE = {A general ergodic theorem},
JOURNAL = {Ann. Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {58},
NUMBER = {1},
MONTH = {July},
YEAR = {1953},
PAGES = {182--191},
DOI = {10.2307/1969828},
NOTE = {MR:0055415. Zbl:0052.11903.},
ISSN = {0003-486X},
}
[17]
A. P. Calderón and A. Zygmund :
“Singular integrals and periodic functions ,”
Studia Math.
14
(1953–1954 ),
pp. 249–271 .
MR
0069310 Zbl
0064.10401 article
Abstract
People
BibTeX
@article {key0069310m,
AUTHOR = {Calder\'on, A. P. and Zygmund, A.},
TITLE = {Singular integrals and periodic functions},
JOURNAL = {Studia Math.},
FJOURNAL = {Studia Mathematica. Polska Akademia
Nauk},
VOLUME = {14},
YEAR = {1953--1954},
PAGES = {249--271},
NOTE = {MR:0069310. Zbl:0064.10401.},
ISSN = {0039-3223},
}
[18]
A. P. Calderón :
“The multipole expansion of radiation fields J. Ration. Mech. Anal.
4 : 5
(1954 ),
pp. 523–537 .
MR
0063540 Zbl
0057.42602 article
Abstract
BibTeX
This paper grew out of an attempt to represent radiation fields as a superposition of fields of multipoles. The existence and uniqueness of a radiation field satisfying the ordinary boundary conditions (prescribed tangential component of the electric field at the boundary) was demonstrated recently by Weyl [1952], Müller [1952] and Saunders [1952] but we avoid using their results partly because our method provides a different approach to the problem and partly because we are interested in relaxing the conditions to be imposed upon the bounding surface as well as those required of the tangential component of the electric field there. This degree of generality is necessary to establish the approximation and expansion theorems that motivated this paper and which are of intrinsic interest. For instance, the expansion theorem provides a means for computing the radiation field by a process involving only integrations over the bounding surface.
@article {key0063540m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {The multipole expansion of radiation
fields},
JOURNAL = {J. Ration. Mech. Anal.},
FJOURNAL = {Journal of Rational Mechanics and Analysis},
VOLUME = {4},
NUMBER = {5},
YEAR = {1954},
PAGES = {523--537},
DOI = {10.1512/iumj.1954.3.53026},
NOTE = {MR:0063540. Zbl:0057.42602.},
ISSN = {1943-5282},
}
[19]
A. P. Calderon :
“Singular integrals ,”
pp. 319–328
in
Segundo symposium sobre algunos problemas matemáticos que se están estudiando en Latino América
[Second symposium on some mathematical problems which have been studied in Latin America ]
(Villavicencio, Argentina, 21–25 July 1954 ).
Centro de Cooperación Científica de la UNESCO para América Latina (Montevideo, Uruguay ),
1954 .
MR
0072986 Zbl
0058.33001 incollection
BibTeX
@incollection {key0072986m,
AUTHOR = {Calderon, A. P.},
TITLE = {Singular integrals},
BOOKTITLE = {Segundo symposium sobre algunos problemas
matem\'aticos que se est\'an estudiando
en {L}atino {A}m\'erica [Second symposium
on some mathematical problems which
have been studied in {L}atin {A}merica]},
PUBLISHER = {Centro de Cooperaci\'on Cient\'\i fica
de la UNESCO para Am\'erica Latina},
ADDRESS = {Montevideo, Uruguay},
YEAR = {1954},
PAGES = {319--328},
NOTE = {(Villavicencio, Argentina, 21--25 July
1954). MR:0072986. Zbl:0058.33001.},
}
[20]
R. F. Arens and A. P. Calderón :
“Analytic functions of Fourier transforms ,”
pp. 39–52
in
Segundo symposium sobre algunos problemas matemáticos que se están estudiando en Latino América
[Second symposium on some mathematical problems which have been studied in Latin America ]
(Villavicencio, Argentina, 21–25 July 1954 ).
Centro de Cooperación Científica de la UNESCO para América Latina (Montevideo, Uruguay ),
1954 .
MR
0069925 Zbl
0058.33202 incollection
People
BibTeX
@incollection {key0069925m,
AUTHOR = {Arens, R. F. and Calder\'on, A. P.},
TITLE = {Analytic functions of {F}ourier transforms},
BOOKTITLE = {Segundo symposium sobre algunos problemas
matem\'aticos que se est\'an estudiando
en {L}atino {A}m\'erica [Second symposium
on some mathematical problems which
have been studied in {L}atin {A}merica]},
PUBLISHER = {Centro de Cooperaci\'on Cient\'\i fica
de la UNESCO para Am\'erica Latina},
ADDRESS = {Montevideo, Uruguay},
YEAR = {1954},
PAGES = {39--52},
NOTE = {(Villavicencio, Argentina, 21--25 July
1954). MR:0069925. Zbl:0058.33202.},
}
[21]
A. P. Calderón and A. Zygmund :
“On a problem of Mihlin Trans. Am. Math. Soc.
78 : 1
(1955 ),
pp. 209–224 .
An addenda to this was paper published in Trans. Am. Math. Soc. 84 :2 (1957)
MR
0068028 Zbl
0065.04104 article
People
BibTeX
@article {key0068028m,
AUTHOR = {Calder\'on, A. P. and Zygmund, A.},
TITLE = {On a problem of {M}ihlin},
JOURNAL = {Trans. Am. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {78},
NUMBER = {1},
YEAR = {1955},
PAGES = {209--224},
DOI = {10.1090/S0002-9947-1955-0068028-9},
NOTE = {An addenda to this was paper published
in \textit{Trans. Am. Math. Soc.} \textbf{84}:2
(1957). MR:0068028. Zbl:0065.04104.},
ISSN = {0002-9947},
}
[22]
R. Arens and A. P. Calderón :
“Analytic functions of several Banach algebra elements Ann. Math. (2)
62 : 2
(September 1955 ),
pp. 204–216 .
MR
0071735 Zbl
0065.34802 article
People
BibTeX
@article {key0071735m,
AUTHOR = {Arens, Richard and Calder\'on, A. P.},
TITLE = {Analytic functions of several {B}anach
algebra elements},
JOURNAL = {Ann. Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {62},
NUMBER = {2},
MONTH = {September},
YEAR = {1955},
PAGES = {204--216},
DOI = {10.2307/1969675},
NOTE = {MR:0071735. Zbl:0065.34802.},
ISSN = {0003-486X},
}
[23]
A. Calderón and A. Devinatz :
“Sur certaines courbes dans l’espace de Hilbert ”
[On certain curves on Hilbert space ],
C. R. Acad. Sci. Paris
241
(1955 ),
pp. 539–541 .
MR
0071741 Zbl
0064.36803 article
People
BibTeX
@article {key0071741m,
AUTHOR = {Calder\'on, Alberto and Devinatz, Allen},
TITLE = {Sur certaines courbes dans l'espace
de {H}ilbert [On certain curves on {H}ilbert
space]},
JOURNAL = {C. R. Acad. Sci. Paris},
FJOURNAL = {Comptes Rendus Hebdomadaires des S\'eances
de l'Acad\'emie des Sciences, Paris},
VOLUME = {241},
YEAR = {1955},
PAGES = {539--541},
NOTE = {MR:0071741. Zbl:0064.36803.},
ISSN = {0001-4036},
}
[24]
A. P. Calderón :
“Sur les mesures invariantes On invariant measures ],
C. R. Acad. Sci. Paris
240
(1955 ),
pp. 1960–1962 .
MR
0069257 Zbl
0064.05102 article
BibTeX
@article {key0069257m,
AUTHOR = {Calder\'on, Alberto P.},
TITLE = {Sur les mesures invariantes [On invariant
measures]},
JOURNAL = {C. R. Acad. Sci. Paris},
FJOURNAL = {Comptes Rendus Hebdomadaires des S\'eances
de l'Acad\'emie des Sciences, Paris},
VOLUME = {240},
YEAR = {1955},
PAGES = {1960--1962},
URL = {http://gallica.bnf.fr/ark:/12148/bpt6k2209n/f469.image},
NOTE = {MR:0069257. Zbl:0064.05102.},
ISSN = {0001-4036},
}
[25]
A. P. Calderón and A. Devinatz :
“Sur certaines courbes à coubure constante dans l’espace de Hilbert ”
[On certain curves of constant curvature on Hilbert space ],
C. R. Acad. Sci. Paris
241
(1955 ),
pp. 586–587 .
MR
0071742 Zbl
0064.36804 article
People
BibTeX
@article {key0071742m,
AUTHOR = {Calder\'on, Alberto P. and Devinatz,
Allen},
TITLE = {Sur certaines courbes \`a coubure constante
dans l'espace de {H}ilbert [On certain
curves of constant curvature on {H}ilbert
space]},
JOURNAL = {C. R. Acad. Sci. Paris},
FJOURNAL = {Comptes Rendus Hebdomadaires des S\'eances
de l'Acad\'emie des Sciences, Paris},
VOLUME = {241},
YEAR = {1955},
PAGES = {586--587},
NOTE = {MR:0071742. Zbl:0064.36804.},
ISSN = {0001-4036},
}
[26]
A. P. Calderón and A. Devinatz :
“On Fourier–Stieltjes transforms Can. J. Math.
7
(1955 ),
pp. 453–461 .
MR
0073747 Zbl
0065.34102 article
Abstract
People
BibTeX
Let \( \mathcal{M} \) be the class of bounded non-decreasing functions defined on the real line which are normalized by the conditions
\[ \phi(-\infty) = 0, \quad \phi(t+0) = \phi(t) .\]
Let \( \mathcal{F} \) be the class of Fourier–Stieltjes transforms of elements of \( \mathcal{M} \) , i.e. the elements of \( \mathcal{M} \) and \( \mathcal{F} \) are connected by the relation
\[ \Phi(x) = \int e^{itx}d\phi(t), \]
where \( \phi \in \mathcal{M} \) and \( \Phi \in \mathcal{F} \) . It is well known, and easy to verify that this mapping from \( \mathcal{M} \) to \( \mathcal{F} \) is one to one [Bochner 1932, p.67, Satz 18].
It is the purpose of this paper to give various topologies to \( \mathcal{F} \) and \( \mathcal{M} \) so that the mapping from \( \mathcal{F} \) to \( \mathcal{M} \) will be continuous or at least continuous at certain points of \( \mathcal{F} \) depending on the topologies. The topologies which we shall have occasion to use are enumerated below.
@article {key0073747m,
AUTHOR = {Calder\'on, A. P. and Devinatz, A.},
TITLE = {On {F}ourier--{S}tieltjes transforms},
JOURNAL = {Can. J. Math.},
FJOURNAL = {Canadian Journal of Mathematics},
VOLUME = {7},
YEAR = {1955},
PAGES = {453--461},
DOI = {10.4153/CJM-1955-049-9},
NOTE = {MR:0073747. Zbl:0065.34102.},
ISSN = {0008-414X},
}
[27]
A. P. Calderón :
“Ideals in Abelian group algebras ,”
pp. 12pp.
in
Symposium on harmonic analysis and related integral transforms: Final technical report
(Ithaca, NY, 23–27 July 1956 ).
Cornell University Department of Mathematics ,
1956 .
incollection
BibTeX
@incollection {key22885773,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Ideals in {A}belian group algebras},
BOOKTITLE = {Symposium on harmonic analysis and related
integral transforms: {F}inal technical
report},
PUBLISHER = {Cornell University Department of Mathematics},
YEAR = {1956},
PAGES = {12pp.},
NOTE = {(Ithaca, NY, 23--27 July 1956).},
}
[28]
A. P. Calderón and A. Zygmund :
“Algebras of certain singular operators Am. J. Math.
78 : 2
(April 1956 ),
pp. 310–320 .
MR
0087810 Zbl
0072.11601 article
Abstract
People
BibTeX
@article {key0087810m,
AUTHOR = {Calder\'on, A. P. and Zygmund, A.},
TITLE = {Algebras of certain singular operators},
JOURNAL = {Am. J. Math.},
FJOURNAL = {American Journal of Mathematics},
VOLUME = {78},
NUMBER = {2},
MONTH = {April},
YEAR = {1956},
PAGES = {310--320},
DOI = {10.2307/2372518},
NOTE = {MR:0087810. Zbl:0072.11601.},
ISSN = {0002-9327},
}
[29]
A. P. Calderón and A. Zygmund :
“On singular integrals Am. J. Math.
78 : 2
(April 1956 ),
pp. 289–309 .
MR
0084633 Zbl
0072.11501 article
Abstract
People
BibTeX
In earlier work [1952] we considered certain singular integrals arising in various problems of Analysis and studied some of their properties. Here we present a new approach to such integrals. Unlike the method used in [1952] it is based on the theory of Hilbert transforms of functions of one variable, but otherwise it is simpler and yields most results obtained previously, under far less restrictive assumptions. Unfortunately some important cases (\( f\in L \) for instance) seem to be beyond its scope. We have been unable to decide whether the corresponding theorems as presented in [1952] can be likewise strengthened.
@article {key0084633m,
AUTHOR = {Calder\'on, A. P. and Zygmund, A.},
TITLE = {On singular integrals},
JOURNAL = {Am. J. Math.},
FJOURNAL = {American Journal of Mathematics},
VOLUME = {78},
NUMBER = {2},
MONTH = {April},
YEAR = {1956},
PAGES = {289--309},
DOI = {10.2307/2372517},
NOTE = {MR:0084633. Zbl:0072.11501.},
ISSN = {0002-9327},
}
[30]
A. P. Calderón and A. Zygmund :
“A note on the interpolation of sublinear operations Am. J. Math.
78 : 2
(April 1956 ),
pp. 282–288 .
MR
0082647 Zbl
0071.33601 article
Abstract
People
BibTeX
@article {key0082647m,
AUTHOR = {Calder\'on, A. P. and Zygmund, A.},
TITLE = {A note on the interpolation of sublinear
operations},
JOURNAL = {Am. J. Math.},
FJOURNAL = {American Journal of Mathematics},
VOLUME = {78},
NUMBER = {2},
MONTH = {April},
YEAR = {1956},
PAGES = {282--288},
DOI = {10.2307/2372516},
NOTE = {MR:0082647. Zbl:0071.33601.},
ISSN = {0002-9327},
}
[31]
A. P. Calderon and A. Zygmund :
“Addenda to the paper ‘On a problem of Mihlin’ Trans. Am. Math. Soc.
84 : 2
(March 1957 ),
pp. 559–560 .
Addenda to a paper published in Trans. Am. Math. Soc. 78 :1 (1955)
MR
0084634 Zbl
0077.27204 article
People
BibTeX
@article {key0084634m,
AUTHOR = {Calderon, A. P. and Zygmund, A.},
TITLE = {Addenda to the paper ``{O}n a problem
of {M}ihlin''},
JOURNAL = {Trans. Am. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {84},
NUMBER = {2},
MONTH = {March},
YEAR = {1957},
PAGES = {559--560},
DOI = {10.2307/1992831},
NOTE = {Addenda to a paper published in \textit{Trans.
Am. Math. Soc.} \textbf{78}:1 (1955).
MR:0084634. Zbl:0077.27204.},
ISSN = {0002-9947},
}
[32]
A.-P. Calderón and A. Zygmund :
“Singular integral operators and differential equations Am. J. Math.
79 : 4
(October 1957 ),
pp. 901–921 .
MR
0100768 Zbl
0081.33502 article
Abstract
People
BibTeX
@article {key0100768m,
AUTHOR = {Calder\'on, A.-P. and Zygmund, A.},
TITLE = {Singular integral operators and differential
equations},
JOURNAL = {Am. J. Math.},
FJOURNAL = {American Journal of Mathematics},
VOLUME = {79},
NUMBER = {4},
MONTH = {October},
YEAR = {1957},
PAGES = {901--921},
DOI = {10.2307/2372441},
NOTE = {MR:0100768. Zbl:0081.33502.},
ISSN = {0002-9327},
}
[33]
A. P. Calderón :
“Uniqueness in the Cauchy problem for partial differential equations Am. J. Math.
80 : 1
(January 1958 ),
pp. 16–36 .
MR
0104925 Zbl
0080.30302 article
BibTeX
@article {key0104925m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Uniqueness in the {C}auchy problem for
partial differential equations},
JOURNAL = {Am. J. Math.},
FJOURNAL = {American Journal of Mathematics},
VOLUME = {80},
NUMBER = {1},
MONTH = {January},
YEAR = {1958},
PAGES = {16--36},
DOI = {10.2307/2372819},
NOTE = {MR:0104925. Zbl:0080.30302.},
ISSN = {0002-9327},
}
[34]
A. Calderón, F. Spitzer, and H. Widom :
“Inversion of Toeplitz matrices Ill. J. Math.
3 : 4
(1959 ),
pp. 490–498 .
MR
0121652 Zbl
0091.11101 article
Abstract
People
BibTeX
This paper deals with the inversion of the Toeplitz matrix \( T = (c_{j-k}) \) , \( j,\, k = 0,\, 1,\dots \) .
@article {key0121652m,
AUTHOR = {Calder\'on, Alberto and Spitzer, Frank
and Widom, Harold},
TITLE = {Inversion of {T}oeplitz matrices},
JOURNAL = {Ill. J. Math.},
FJOURNAL = {Illinois Journal of Mathematics},
VOLUME = {3},
NUMBER = {4},
YEAR = {1959},
PAGES = {490--498},
URL = {http://projecteuclid.org/euclid.ijm/1255455456},
NOTE = {MR:0121652. Zbl:0091.11101.},
ISSN = {0019-2082},
}
[35]
A.-P. Calderón and A. Zygmund :
“A note on local properties of solutions of elliptic differential equations Proc. Natl. Acad. Sci. U.S.A.
46 : 10
(October 1960 ),
pp. 1385–1389 .
An expanded version of this was published in Studia Math. 20 :2 (1961)
MR
0140829 Zbl
0196.40501 article
Abstract
People
BibTeX
We formulate here pointwise estimates for solutions of elliptic partial differential equations and systems. The results obtained differ from the familiar ones in that they give information about the behavior of solutions at individual points. More specifically, we obtain two kinds of results. On the one hand, we establish inequalities for solutions and their derivatives at isolated individual points. On the other, we also obtain results of the “almost everywhere” type.
@article {key0140829m,
AUTHOR = {Calder\'on, A.-P. and Zygmund, A.},
TITLE = {A note on local properties of solutions
of elliptic differential equations},
JOURNAL = {Proc. Natl. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {46},
NUMBER = {10},
MONTH = {October},
YEAR = {1960},
PAGES = {1385--1389},
DOI = {10.1073/pnas.46.10.1385},
NOTE = {An expanded version of this was published
in \textit{Studia Math.} \textbf{20}:2
(1961). MR:0140829. Zbl:0196.40501.},
ISSN = {0027-8424},
}
[36]
A. P. Calderón :
Integrales singulares y sus aplicaciones a ecuaciones diferenciales hiperbolicas
[Singular integrals and their applications to hyperbolic differential equations ].
Cursos y Seminarios de Matemática 3 .
Universidad de Buenos Aires ,
1960 .
MR
0123834 Zbl
0096.06702 book
BibTeX
@book {key0123834m,
AUTHOR = {Calder\'on, Alberto P.},
TITLE = {Integrales singulares y sus aplicaciones
a ecuaciones diferenciales hiperbolicas
[Singular integrals and their applications
to hyperbolic differential equations]},
SERIES = {Cursos y Seminarios de Matem\'atica},
NUMBER = {3},
PUBLISHER = {Universidad de Buenos Aires},
YEAR = {1960},
PAGES = {121},
NOTE = {MR:0123834. Zbl:0096.06702.},
ISSN = {0524-9643},
}
[37]
A.-P. Calderón and A. Zygmund :
“Local properties of solutions of elliptic partial differential equations Studia Math.
20 : 2
(1961 ),
pp. 171–225 .
This expands on an article published in Proc. Natl. Acad. Sci. U.S.A. 46 :10 (1960)
MR
0136849 Zbl
0099.30103 article
Abstract
People
BibTeX
The purpose of this paper is to establish pointwise estimates for solutions of elliptic partial differential equations and systems. The results presented here differ from the familiar ones in that they give information about the behavior of solutions at individual points. More specifically, we obtain two kinds of results. On the one hand, we establish inequalities for solutions and their derivatives at isolated individual points. On the other, we also obtain results of the “almost everywhere” type.
@article {key0136849m,
AUTHOR = {Calder\'on, A.-P. and Zygmund, A.},
TITLE = {Local properties of solutions of elliptic
partial differential equations},
JOURNAL = {Studia Math.},
FJOURNAL = {Studia Mathematica. Polska Akademia
Nauk},
VOLUME = {20},
NUMBER = {2},
YEAR = {1961},
PAGES = {171--225},
URL = {http://matwbn.icm.edu.pl/ksiazki/sm/sm20/sm20113.pdf},
NOTE = {This expands on an article published
in \textit{Proc. Natl. Acad. Sci. U.S.A.}
\textbf{46}:10 (1960). MR:0136849. Zbl:0099.30103.},
ISSN = {0039-3223},
}
[38]
A. P. Calderón :
“Lebesgue spaces of differentiable functions and distributions ,”
pp. 33–49
in
Partial differential equations
(Berkeley, CA, 21–22 April 1960 ).
Edited by C. B. Morrey, Jr.
Proceedings of Symposia in Pure Mathematics 4 .
American Mathematical Society (Providence, RI ),
1961 .
MR
0143037 Zbl
0195.41103 incollection
People
BibTeX
Charles Bradfield Morrey, Jr.
Related
@incollection {key0143037m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Lebesgue spaces of differentiable functions
and distributions},
BOOKTITLE = {Partial differential equations},
EDITOR = {Morrey, Jr., Charles B.},
SERIES = {Proceedings of Symposia in Pure Mathematics},
NUMBER = {4},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1961},
PAGES = {33--49},
NOTE = {(Berkeley, CA, 21--22 April 1960). MR:0143037.
Zbl:0195.41103.},
ISSN = {0082-0717},
}
[39]
A.-P. Calderón and A. Zygmund :
“On the differentiability of functions which are of bounded variation in Tonelli’s sense Rev. Un. Mat. Argentina
20
(1962 ),
pp. 102–121 .
MR
0151557 Zbl
0116.31804 article
Abstract
People
BibTeX
@article {key0151557m,
AUTHOR = {Calder\'on, A.-P. and Zygmund, A.},
TITLE = {On the differentiability of functions
which are of bounded variation in {T}onelli's
sense},
JOURNAL = {Rev. Un. Mat. Argentina},
FJOURNAL = {Revista de la Uni\'on Matem\'atica Argentina},
VOLUME = {20},
YEAR = {1962},
PAGES = {102--121},
URL = {http://inmabb.criba.edu.ar/revuma/pdf/v20/p102-121.pdf},
NOTE = {MR:0151557. Zbl:0116.31804.},
ISSN = {0041-6932},
}
[40]
A. Benedek, A. P. Calderón, and R. Panzone :
“Convolution operators on Banach space valued functions Proc. Natl. Acad. Sci. U.S.A.
48 : 3
(March 1962 ),
pp. 356–365 .
MR
0133653 Zbl
0103.33402 article
Abstract
People
BibTeX
The purpose of this paper is to obtain systematically certain classical inequalities concerning the Hilbert transform, the function \( g \) of Littlewood and Paley, their generalizations to several variables, and related results. This we accomplish by establishing certain inequalities for convolution operators on Banach space valued functions.
@article {key0133653m,
AUTHOR = {Benedek, A. and Calder\'on, A. P. and
Panzone, R.},
TITLE = {Convolution operators on {B}anach space
valued functions},
JOURNAL = {Proc. Natl. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {48},
NUMBER = {3},
MONTH = {March},
YEAR = {1962},
PAGES = {356--365},
DOI = {10.1073/pnas.48.3.356},
NOTE = {MR:0133653. Zbl:0103.33402.},
ISSN = {0027-8424},
}
[41]
A. P. Calderón :
“Existence and uniqueness theorems for systems of partial differential equations ,”
pp. 147–195
in
Fluid dynamics and applied mathematics
(College Park, MD, 28–29 April 1961 ).
Edited by J. B. Diaz and S. Bai .
Gordon and Breach (New York ),
1962 .
MR
0156078 Zbl
0147.08202 incollection
People
BibTeX
@incollection {key0156078m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Existence and uniqueness theorems for
systems of partial differential equations},
BOOKTITLE = {Fluid dynamics and applied mathematics},
EDITOR = {Diaz, Joaquin B. and Bai, Shiyi},
PUBLISHER = {Gordon and Breach},
ADDRESS = {New York},
YEAR = {1962},
PAGES = {147--195},
NOTE = {(College Park, MD, 28--29 April 1961).
MR:0156078. Zbl:0147.08202.},
}
[42]
A. P. Calderón :
“Intermediate spaces and interpolation Studia Math. Ser. Spec.
1
(1963 ),
pp. 31–34 .
MR
0147896 Zbl
0124.31803 article
Abstract
BibTeX
@article {key0147896m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Intermediate spaces and interpolation},
JOURNAL = {Studia Math. Ser. Spec.},
FJOURNAL = {Studia Mathematica, Seria Specjalna},
VOLUME = {1},
YEAR = {1963},
PAGES = {31--34},
URL = {http://matwbn.icm.edu.pl/ksiazki/sm/sm23/sm23424.pdf},
NOTE = {MR:0147896. Zbl:0124.31803.},
ISSN = {0585-5357},
}
[43]
A. P. Calderón :
“Boundary value problems for elliptic equations ,”
pp. 303–304
in
Outlines of the joint Soviet–American symposium on partial differential equations
(Novosibirsk, August 1963 ).
Akademiia Nauk SSSR Sibirskoe Otdelenie (Moscow ),
1963 .
MR
0203254 incollection
BibTeX
@incollection {key0203254m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Boundary value problems for elliptic
equations},
BOOKTITLE = {Outlines of the joint {S}oviet--{A}merican
symposium on partial differential equations},
PUBLISHER = {Akademiia Nauk SSSR Sibirskoe Otdelenie},
ADDRESS = {Moscow},
YEAR = {1963},
PAGES = {303--304},
NOTE = {(Novosibirsk, August 1963). MR:0203254.},
}
[44]
A.-P. Calderón and A. Zygmund :
“On higher gradients of harmonic functions ,”
pp. 57–60
in
Outlines of the joint Soviet-American symposium on partial differential equations
(Novosibirsk, August 1963 ).
Academy of Sciences of the USSR, Siberian Branch (Moscow ),
1963 .
A version of this was later published in Studia Math. 24 :2 (1964)
MR
0214798 incollection
People
BibTeX
@incollection {key0214798m,
AUTHOR = {Calder\'on, A.-P. and Zygmund, A.},
TITLE = {On higher gradients of harmonic functions},
BOOKTITLE = {Outlines of the joint {S}oviet-{A}merican
symposium on partial differential equations},
PUBLISHER = {Academy of Sciences of the USSR, Siberian
Branch},
ADDRESS = {Moscow},
YEAR = {1963},
PAGES = {57--60},
NOTE = {(Novosibirsk, August 1963). A version
of this was later published in \textit{Studia
Math.} \textbf{24}:2 (1964). MR:0214798.},
}
[45]
A.-P. Calderón and A. Zygmund :
“On higher gradients of harmonic functions Studia Math.
24 : 2
(1964 ),
pp. 211–226 .
An earlier version of this was published in Outlines of the joint Soviet-American symposium on partial differential equations (1963)
MR
0167631 Zbl
0168.37002 article
People
BibTeX
@article {key0167631m,
AUTHOR = {Calder\'on, A.-P. and Zygmund, A.},
TITLE = {On higher gradients of harmonic functions},
JOURNAL = {Studia Math.},
FJOURNAL = {Studia Mathematica. Polska Akademia
Nauk},
VOLUME = {24},
NUMBER = {2},
YEAR = {1964},
PAGES = {211--226},
URL = {http://matwbn.icm.edu.pl/ksiazki/sm/sm24/sm24112.pdf},
NOTE = {An earlier version of this was published
in \textit{Outlines of the joint Soviet-American
symposium on partial differential equations}
(1963). MR:0167631. Zbl:0168.37002.},
ISSN = {0039-3223},
}
[46]
A. P. Calderón :
“Intermediate spaces and interpolation, the complex method Studia Math.
24 : 2
(1964 ),
pp. 113–190 .
MR
0167830 Zbl
0204.13703 article
Abstract
BibTeX
In this paper we discuss in detail the so called complex method of interpolation which was originally introduced by the author in [1963], and later, independently, by J. L. Lions in [1960].
@article {key0167830m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Intermediate spaces and interpolation,
the complex method},
JOURNAL = {Studia Math.},
FJOURNAL = {Studia Mathematica. Polska Akademia
Nauk. Instytut Matematyczny},
VOLUME = {24},
NUMBER = {2},
YEAR = {1964},
PAGES = {113--190},
URL = {http://matwbn.icm.edu.pl/ksiazki/sm/sm24/sm24110.pdf},
NOTE = {MR:0167830. Zbl:0204.13703.},
ISSN = {0039-3223},
}
[47]
A. P. Calderón :
“Commutators of singular integral operators Proc. Natl. Acad. Sci. U.S.A.
53 : 5
(May 1965 ),
pp. 1092–1099 .
MR
0177312 Zbl
0151.16901 article
Abstract
BibTeX
Let
\[ A(f) = \lim_{\varepsilon \to 0} \int_{|x-y| > \varepsilon}k(x-y)f(y)\,dy, \]
where \( x \) , \( y \) are points in \( n \) -dimensional Euclidean space \( R^n \) and \( k(x) \) is a homogeneous function of degree \( -n \) with mean value zero on \( |x| = 1 \) , and let
\[ B(f) = b(x)f(x) .\]
It is well known [Calderón and Zygmund 1957] that if \( k \) and \( b \) are sufficiently smooth and \( b \) is bounded, then
\[ (AB - BA)(\partial/\partial x_j) \quad\text{and}\quad (\partial/\partial x_j)(AB - BA) \]
are bounded operators in \( L^p \) , \( 1 < p < \infty \) . The purpose of the present note is to extend and strengthen the preceding result and establish some related facts of independent interest.
@article {key0177312m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Commutators of singular integral operators},
JOURNAL = {Proc. Natl. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {53},
NUMBER = {5},
MONTH = {May},
YEAR = {1965},
PAGES = {1092--1099},
DOI = {10.1073/pnas.53.5.1092},
NOTE = {MR:0177312. Zbl:0151.16901.},
ISSN = {0027-8424},
}
[48]
A. P. Calderón :
“Singular integrals Bull. Am. Math. Soc.
72 : 3
(1966 ),
pp. 427–465 .
MR
0209918 Zbl
0151.16902 article
Abstract
BibTeX
@article {key0209918m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Singular integrals},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {72},
NUMBER = {3},
YEAR = {1966},
PAGES = {427--465},
DOI = {10.1090/S0002-9904-1966-11492-1},
NOTE = {MR:0209918. Zbl:0151.16902.},
ISSN = {0002-9904},
}
[49]
A. P. Calderón :
“Spaces between \( L^1 \) and \( L^{\infty} \) and the theorem of Marcinkiewicz Studia Math.
26 : 3
(1966 ),
pp. 273–299 .
MR
0203444 Zbl
0149.09203 article
Abstract
BibTeX
@article {key0203444m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Spaces between \$L^1\$ and \$L^{\infty}\$
and the theorem of {M}arcinkiewicz},
JOURNAL = {Studia Math.},
FJOURNAL = {Studia Mathematica. Polska Akademia
Nauk. Instytut Matematyczny},
VOLUME = {26},
NUMBER = {3},
YEAR = {1966},
PAGES = {273--299},
URL = {http://matwbn.icm.edu.pl/ksiazki/sm/sm26/sm26123.pdf},
NOTE = {MR:0203444. Zbl:0149.09203.},
ISSN = {0039-3223},
}
[50]
A. P. Calderón :
Estimates for integral operators .
Technical report 65-1866 ,
U.S.A.F. Office of Scientific Research ,
1966 .
techreport
BibTeX
@techreport {key91256151,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Estimates for integral operators},
NUMBER = {65-1866},
INSTITUTION = {U.S.A.F. Office of Scientific Research},
YEAR = {1966},
PAGES = {3--12},
}
[51]
Singular integrals
(Chicago, IL, 20–22 April 1966 ).
Edited by A. P. Calderón .
Proceedings of Symposia in Pure Mathematics 10 .
American Mathematical Society (Providence, RI ),
1967 .
MR
0230584 Zbl
0162.00206 book
BibTeX
@book {key0230584m,
TITLE = {Singular integrals},
EDITOR = {Calder\'on, Alberto P.},
SERIES = {Proceedings of Symposia in Pure Mathematics},
NUMBER = {10},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1967},
PAGES = {vi+375},
NOTE = {(Chicago, IL, 20--22 April 1966). MR:0230584.
Zbl:0162.00206.},
ISSN = {0082-0717},
}
[52]
A. P. Calderón :
“Algebras of singular integral operators ,”
pp. 18–55
in
Singular integrals
(Chicago, IL, 20–22 April 1966 ).
Edited by A. P. Calderón .
Proceedings of Symposia in Pure Mathematics 10 .
American Mathematical Society (Providence, RI ),
1967 .
Also published in Trudy Mezhdunarodnogo Kongressa Matematikov (1968)
MR
0394309 Zbl
0182.47402 incollection
Abstract
BibTeX
In dealing with differential operator with non-smooth coefficients one is led to consider pseudo-differential operators and singular integral operators with non-smooth symbols and kernels. Such pseudo-differential operators, however, do not have desirable algebraic properties. This becomes evident if one observes that in particular differential operators cannot be composed freely unless one assumes their coefficients to be infinitely differentiable. The situation is different with singular integral operators. Here it is possible to construct a theory, which is fairly general as far as regularity assumptions is concerned, preserving at the same time an algebra structure and a relatively simple approximate functional calculus. In what follows we will give a brief description.
@incollection {key0394309m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Algebras of singular integral operators},
BOOKTITLE = {Singular integrals},
EDITOR = {Calder\'on, A. P.},
SERIES = {Proceedings of Symposia in Pure Mathematics},
NUMBER = {10},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1967},
PAGES = {18--55},
NOTE = {(Chicago, IL, 20--22 April 1966). Also
published in \textit{Trudy Mezhdunarodnogo
Kongressa Matematikov} (1968). MR:0394309.
Zbl:0182.47402.},
ISSN = {0082-0717},
}
[53]
A. P. Calderón, M. Weiss, and A. Zygmund :
“On the existence of singular integrals ,”
pp. 56–73
in
Singular integrals
(Chicago, 20–22 April 1966 ).
Edited by A. P. Calderón .
Proceedings of Symposia in Pure Mathematics 10 .
American Mathematical Society (Providence, RI ),
1967 .
An addendum to this article was published in Studia Math. 46 :3 (1973)
MR
0338709 Zbl
0167.12202 incollection
People
BibTeX
@incollection {key0338709m,
AUTHOR = {Calder\'on, A. P. and Weiss, Mary and
Zygmund, A.},
TITLE = {On the existence of singular integrals},
BOOKTITLE = {Singular integrals},
EDITOR = {Calder\'on, Alberto P.},
SERIES = {Proceedings of Symposia in Pure Mathematics},
NUMBER = {10},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1967},
PAGES = {56--73},
NOTE = {(Chicago, 20--22 April 1966). An addendum
to this article was published in \textit{Studia
Math.} \textbf{46}:3 (1973). MR:0338709.
Zbl:0167.12202.},
ISSN = {0082-0717},
}
[54]
A. P. Calderón :
“The analytic calculation of the index of elliptic equations Proc. Natl. Acad. Sci. U.S.A.
57 : 5
(May 1967 ),
pp. 1193–1194 .
MR
0211031 Zbl
0152.11402 article
Abstract
BibTeX
@article {key0211031m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {The analytic calculation of the index
of elliptic equations},
JOURNAL = {Proc. Natl. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {57},
NUMBER = {5},
MONTH = {May},
YEAR = {1967},
PAGES = {1193--1194},
DOI = {10.1073/pnas.57.5.1193},
NOTE = {MR:0211031. Zbl:0152.11402.},
ISSN = {0027-8424},
}
[55]
A. P. Calderón :
“Algebras of singular integral operators 393–395
in
Trudy Mezhdunarodnogo Kongressa Matematikov
[Proceedings of the International Congress of Mathematicians ]
(Moscow, 16–26 August 1966 ),
vol. 1 .
Edited by I. G. Petrovsky .
Mir (Moscow ),
1968 .
Also published in Singular integrals (1967)
MR
0248563 Zbl
0187.39401 incollection
Abstract
People
BibTeX
In dealing with differential operator with non-smooth coefficients one is led to consider pseudo-differential operators and singular integral operators with non-smooth symbols and kernels. Such pseudo-differential operators, however, do not have desirable algebraic properties. This becomes evident if one observes that in particular differential operators cannot be composed freely unless one assumes their coefficients to be infinitely differentiable. The situation is different with singular integral operators. Here it is possible to construct a theory, which is fairly general as far as regularity assumptions is concerned, preserving at the same time an algebra structure and a relatively simple approximate functional calculus. In what follows we will give a brief description.
@incollection {key0248563m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Algebras of singular integral operators},
BOOKTITLE = {Trudy {M}ezhdunarodnogo {K}ongressa
{M}atematikov [Proceedings of the {I}nternational
{C}ongress of {M}athematicians]},
EDITOR = {Petrovsky, I. G.},
VOLUME = {1},
PUBLISHER = {Mir},
ADDRESS = {Moscow},
YEAR = {1968},
PAGES = {393--395},
URL = {http://www.mathunion.org/ICM/ICM1966.1/Main/icm1966.1.0393.0394.ocr.pdf},
NOTE = {(Moscow, 16--26 August 1966). Also published
in \textit{Singular integrals} (1967).
MR:0248563. Zbl:0187.39401.},
}
[56]
A. P. Calderón :
“Ergodic theory and translation-invariant operators Proc. Natl. Acad. Sci. U.S.A.
59 : 2
(February 1968 ),
pp. 349–353 .
MR
0227354 Zbl
0185.21806 article
Abstract
BibTeX
It has been known for a long time that there is a close connection between the ergodic theorem and certain facts about functions on the real line, such as the maximal theory of Hardy and Littlewood and the differentiation theorem for indefinite integrals. In more recent times Cotlar has shown that theorems on singular integrals can be generalized and put in the framework of ergodic theory. The purpose of this note is to exhibit a class of results on translation-invariant operators which can be automatically rephrased in such a framework. In this light the maximal ergodic theorem appears as an immediate consequence of the maximal theorem of Hardy and Littlewood, and the results of Cotlar as following from the ordinary theorems on singular integrals. For the sake of simplicity we shall consider only groups of measure-preserving transformations depending on a single real parameter \( t \) ; as the reader will immediately see, our statements and their proofs extend without modification to continuous or discrete abelian groups depending on finitely many parameters. Extension of these results to semigroups is discussed briefly at the end of the paper.
@article {key0227354m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Ergodic theory and translation-invariant
operators},
JOURNAL = {Proc. Natl. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {59},
NUMBER = {2},
MONTH = {February},
YEAR = {1968},
PAGES = {349--353},
DOI = {10.1073/pnas.59.2.349},
NOTE = {MR:0227354. Zbl:0185.21806.},
ISSN = {0027-8424},
}
[57]
A. P. Calderón :
“A priori estimates for singular integral operators 85–141
in
Pseudo-differential operators
(Stresa, Italy, 26 August–3 September 1968 ).
Edited by L. Nirenberg .
Edizioni Cremonese (Rome ),
1969 .
MR
0256215 incollection
Abstract
People
BibTeX
@incollection {key0256215m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {A priori estimates for singular integral
operators},
BOOKTITLE = {Pseudo-differential operators},
EDITOR = {Nirenberg, Louis},
PUBLISHER = {Edizioni Cremonese},
ADDRESS = {Rome},
YEAR = {1969},
PAGES = {85--141},
DOI = {10.1007/978-3-642-11074-0_4},
NOTE = {(Stresa, Italy, 26 August--3 September
1968). MR:0256215.},
}
[58]
A. P. Calderón :
“Estimates for singular integral operators ,”
pp. 149–159
in
Lectures in differential equations ,
vol. 1 .
Edited by A. K. Aziz .
Van Nostrand Mathematical Studies .
Van Nostrand (New York ),
1969 .
MR
0247532 Zbl
0181.38803 incollection
People
BibTeX
@incollection {key0247532m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Estimates for singular integral operators},
BOOKTITLE = {Lectures in differential equations},
EDITOR = {Aziz, Abdul Kadir},
VOLUME = {1},
SERIES = {Van Nostrand Mathematical Studies},
PUBLISHER = {Van Nostrand},
ADDRESS = {New York},
YEAR = {1969},
PAGES = {149--159},
NOTE = {MR:0247532. Zbl:0181.38803.},
}
[59]
A. P. Calderón :
“Uniqueness of distributions Rev. Un. Mat. Argentina
25 : 1–2
(1970 ),
pp. 37–65 .
Dedicated to Alberto González Domínguez.
MR
0343018 Zbl
0251.46045 article
People
BibTeX
@article {key0343018m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Uniqueness of distributions},
JOURNAL = {Rev. Un. Mat. Argentina},
FJOURNAL = {Revista de la Uni\'on Matem\'atica Argentina},
VOLUME = {25},
NUMBER = {1--2},
YEAR = {1970},
PAGES = {37--65},
URL = {http://inmabb.criba.edu.ar/revuma/pdf/v25n1y2/p037-065.pdf},
NOTE = {Dedicated to Alberto Gonz\'alez Dom\'{\i}nguez.
MR:0343018. Zbl:0251.46045.},
ISSN = {0041-6932},
}
[60]
A. P. Calderón and R. Vaillancourt :
“On the boundedness of pseudo-differential operators J. Math. Soc. Japan
23 : 2
(1971 ),
pp. 374–378 .
MR
0284872 Zbl
0203.45903 article
Abstract
People
BibTeX
In this note we show that a bounded symbol \( p(x,\xi) \) with bounded derivatives
\[ \partial_x^{\beta}\partial_{\xi}^{\alpha}p(x,\xi) \]
defines a bounded pseudo-differential operator
\[ (Pf)(x) = (2\pi)^{-n}\int e^{ix\cdot\xi}p(x,\xi)\hat{f}(\xi)\,d\xi \]
in \( L^2 \) . Symbols \( p(x,\xi) \) of the class \( S_{\rho,0}^0 \) , \( \rho > 0 \) , defined in [Hörmander 1967] by the inequality
\[ |\partial_x^{\beta}\partial_{\xi}^{\alpha}p(x,\xi)|\leqq C_{\alpha\beta}(1+|\xi|)^{-\rho|\alpha|} \]
are of this form. The result is new for \( \rho=0 \) . Our proof makes use of a modification of a lemma of Cotlar (see [Knapp and Stein 1969]) for almost orthogonal operators in a Hilbert space.
@article {key0284872m,
AUTHOR = {Calder\'on, Alberto P. and Vaillancourt,
R\'emi},
TITLE = {On the boundedness of pseudo-differential
operators},
JOURNAL = {J. Math. Soc. Japan},
FJOURNAL = {Journal of the Mathematical Society
of Japan},
VOLUME = {23},
NUMBER = {2},
YEAR = {1971},
PAGES = {374--378},
DOI = {10.2969/jmsj/02320374},
NOTE = {MR:0284872. Zbl:0203.45903.},
ISSN = {0025-5645},
}
[61]
A. P. Calderón :
“Estimates for singular integral operators in terms of maximal functions ,”
Studia Math.
44 : 6
(1972 ),
pp. 563–582 .
Dedicated to Professor Antoni Zygmund.
MR
0348555 Zbl
0222.44007 article
Abstract
People
BibTeX
Various maximal functions \( M(f,x) \) are associated with certain distributions in
\[ \bigcup_{k > 0}L_{-k}^p,\qquad 1 < p < \infty.\]
They are slight modifications and generalizations of the following function associated with a function \( f(x) \) of a single variable
\[ \sup_{t > 0}\frac{1}{t}\Bigl|\int_0^tf(x+s) \,ds\Bigr|. \]
It is shown that, if \( K \) is a singular integral operator, it is possible to estimate \( M(Kf,x) \) in terms of \( M(f,x) \) provided the latter is finite and integrable to some power \( p \) , \( p < \infty \) , outside a set of finite measure.
@article {key0348555m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Estimates for singular integral operators
in terms of maximal functions},
JOURNAL = {Studia Math.},
FJOURNAL = {Studia Mathematica. Polska Akademia
Nauk. Instytut Matematyczny},
VOLUME = {44},
NUMBER = {6},
YEAR = {1972},
PAGES = {563--582},
NOTE = {Dedicated to Professor Antoni Zygmund.
MR:0348555. Zbl:0222.44007.},
ISSN = {0039-3223},
}
[62]
A. P. Calderón and R. Vaillancourt :
“A class of bounded pseudo-differential operators Proc. Natl. Acad. Sci. U.S.A.
69 : 5
(May 1972 ),
pp. 1185–1187 .
MR
0298480 Zbl
0244.35074 article
Abstract
People
BibTeX
Pseudo-differential operators of order \( -M \) and type \( \rho \) , \( \delta_1 \) , \( \delta_2 \) are shown to be bounded in \( L^2 \) provided that
\[ 0 \leq \rho \leq \delta_1 < 1, \quad 0 \leq \rho \leq \delta_2 < 1, \quad\text{and}\quad \frac{M}{n} \geq \frac{1}{2}(\delta_1 + \delta_2) - \rho .\]
@article {key0298480m,
AUTHOR = {Calder\'on, Alberto P. and Vaillancourt,
R{\'e}mi},
TITLE = {A class of bounded pseudo-differential
operators},
JOURNAL = {Proc. Natl. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {69},
NUMBER = {5},
MONTH = {May},
YEAR = {1972},
PAGES = {1185--1187},
DOI = {10.1073/pnas.69.5.1185},
NOTE = {MR:0298480. Zbl:0244.35074.},
ISSN = {0027-8424},
}
[63]
A. P. Calderón :
“A note on biquadratic forms Linear Algebra Appl.
7 : 2
(1973 ),
pp. 175–177 .
MR
0320039 Zbl
0258.15016 article
Abstract
BibTeX
@article {key0320039m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {A note on biquadratic forms},
JOURNAL = {Linear Algebra Appl.},
FJOURNAL = {Linear Algebra and Applications},
VOLUME = {7},
NUMBER = {2},
YEAR = {1973},
PAGES = {175--177},
DOI = {10.1016/0024-3795(73)90052-9},
NOTE = {MR:0320039. Zbl:0258.15016.},
ISSN = {0024-3795},
}
[64]
A. P. Calderón and A. Zygmund :
“Addendum to the paper ‘On singular integrals’ Studia Math.
46 : 3
(1973 ),
pp. 297–299 .
Addendum to an article published in Singular integrals (1967)Studia Math. 47 :3 (1973)
MR
0338710 Zbl
0263.44003 article
Abstract
People
BibTeX
Let \( x\in E^n \) ,
\[ \tilde{f}_{\varepsilon}(x) = (K_{\varepsilon}* f)(x) ,\]
where
\[ K_{\varepsilon}(x) = \Lambda(x)|x|^{-n} \]
for \( |x| > \varepsilon \) and is 0 otherwise, and \( \Lambda(x) \) is a homogeneous function of degree 0 whose mean value over the unit sphere \( (\Sigma)|x| = 1 \) is 0. Let \( \omega_1(\delta) \) be the “rotational” modulus of continuity of \( \Lambda \) in the metric \( L^1 \) :
\[ \omega_1(\delta) = \sup_{|p| < \delta}\int_{\Sigma}|\Lambda(\rho x) - \Lambda(x)|\,d\sigma ,\]
where \( \rho \) is an arbitrary rotation on \( \Sigma \) , \( |\rho| \) its magnitude, and \( d\sigma \) the element of surface area. The note clarifies a proof of the following theorem: If \( \omega_1(\delta) \) satisfies the Dini condition, i.e.
\[ \int_0^1\delta^{-1}\omega_1(\delta)\,d\delta < \infty ,\]
then the operation
\[ \sup_{\varepsilon}|\tilde{f}_{\varepsilon}(x)| = Tf \]
is of weak type \( (1,1) \) .
@article {key0338710m,
AUTHOR = {Calder\'on, A. P. and Zygmund, A.},
TITLE = {Addendum to the paper ``{O}n singular
integrals''},
JOURNAL = {Studia Math.},
FJOURNAL = {Studia Mathematica. Polska Akademia
Nauk},
VOLUME = {46},
NUMBER = {3},
YEAR = {1973},
PAGES = {297--299},
URL = {http://matwbn.icm.edu.pl/ksiazki/sm/sm46/sm46125.pdf},
NOTE = {Addendum to an article published in
\textit{Singular integrals} (1967).
Errata for this addendum were published
in \textit{Studia Math.} \textbf{47}:3
(1973). MR:0338710. Zbl:0263.44003.},
ISSN = {0039-3223},
}
[65]
A. P. Calderón and A. Zygmund :
“Errata: ‘Addendum to the paper ‘On singular integrals’ ’ Studia Math.
47 : 3
(1973 ),
pp. 305 .
Errata for an addendum published in Studia Math. 46 :3 (1973)
MR
0338711 Zbl
0263.44004 article
People
BibTeX
@article {key0338711m,
AUTHOR = {Calder{\'o}n, A. P. and Zygmund, A.},
TITLE = {Errata: ``{A}ddendum to the paper ``{O}n
singular integrals''''},
JOURNAL = {Studia Math.},
FJOURNAL = {Studia Mathematica. Polska Akademia
Nauk},
VOLUME = {47},
NUMBER = {3},
YEAR = {1973},
PAGES = {305},
URL = {http://matwbn.icm.edu.pl/ksiazki/sm/sm47/sm47123.pdf},
NOTE = {Errata for an addendum published in
\textit{Studia Math.} \textbf{46}:3
(1973). MR:0338711. Zbl:0263.44004.},
ISSN = {0039-3223},
}
[66]
A. P. Calderón and A. Torchinsky :
“Parabolic maximal functions associated with a distribution Adv. Math.
16 : 1
(April 1975 ),
pp. 1–64 .
MR
0417687 Zbl
0315.46037 article
Abstract
People
BibTeX
In this paper we extend some interesting recent results of Burkholder, Gundy and Silverstein [1971], and Fefferman and Stein [1972] concerning the classes HP of analytic functions in a halfplane or harmonic functions in a halfspace.
@article {key0417687m,
AUTHOR = {Calder\'on, A. P. and Torchinsky, A.},
TITLE = {Parabolic maximal functions associated
with a distribution},
JOURNAL = {Adv. Math.},
FJOURNAL = {Advances in Mathematics},
VOLUME = {16},
NUMBER = {1},
MONTH = {April},
YEAR = {1975},
PAGES = {1--64},
DOI = {10.1016/0001-8708(75)90099-7},
NOTE = {MR:0417687. Zbl:0315.46037.},
ISSN = {0001-8708},
}
[67]
A. P. Calderón :
“On an integral of Marcinkiewicz Studia Math.
57 : 3
(1976 ),
pp. 279–284 .
A correction to this article was published in Studia Math. 62 :1 (1978)
MR
0442578 Zbl
0341.44008 article
Abstract
BibTeX
@article {key0442578m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {On an integral of {M}arcinkiewicz},
JOURNAL = {Studia Math.},
FJOURNAL = {Studia Mathematica. Polska Akademia
Nauk. Instytut Matematyczny},
VOLUME = {57},
NUMBER = {3},
YEAR = {1976},
PAGES = {279--284},
URL = {http://matwbn.icm.edu.pl/ksiazki/sm/sm57/sm57121.pdf},
NOTE = {A correction to this article was published
in \textit{Studia Math.} \textbf{62}:1
(1978). MR:0442578. Zbl:0341.44008.},
ISSN = {0039-3223},
}
[68]
A. P. Calderón :
“Inequalities for the maximal function relative to a metric Studia Math.
57 : 3
(1976 ),
pp. 297–306 .
MR
0442579 Zbl
0341.44007 article
Abstract
BibTeX
@article {key0442579m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Inequalities for the maximal function
relative to a metric},
JOURNAL = {Studia Math.},
FJOURNAL = {Studia Mathematica. Polska Akademia
Nauk. Instytut Matematyczny},
VOLUME = {57},
NUMBER = {3},
YEAR = {1976},
PAGES = {297--306},
URL = {http://matwbn.icm.edu.pl/ksiazki/sm/sm57/sm57123.pdf},
NOTE = {MR:0442579. Zbl:0341.44007.},
ISSN = {0039-3223},
}
[69]
A. P. Calderón and A. Torchinsky :
“Classes of distributions with parabolic maximal functions in \( L^p(\mathbf{R}^n) \) ,”
pp. 27–38
in
Functional analysis
(São Paulo, July 1974 ).
Edited by D. Guedes de Figueiredo .
Lecture Notes in Pure and Applied Mathematics 18 .
Dekker (New York ),
1976 .
MR
0632015 Zbl
0352.46027 incollection
People
BibTeX
@incollection {key0632015m,
AUTHOR = {Calder\'on, Alberto P. and Torchinsky,
Alberto},
TITLE = {Classes of distributions with parabolic
maximal functions in \$L^p(\mathbf{R}^n)\$},
BOOKTITLE = {Functional analysis},
EDITOR = {Guedes de Figueiredo, Djairo},
SERIES = {Lecture Notes in Pure and Applied Mathematics},
NUMBER = {18},
PUBLISHER = {Dekker},
ADDRESS = {New York},
YEAR = {1976},
PAGES = {27--38},
NOTE = {(S\~{a}o Paulo, July 1974). MR:0632015.
Zbl:0352.46027.},
ISSN = {0075-8469},
ISBN = {9780824763343},
}
[70]
A. P. Calderón :
“An inequality for integrals Studia Math.
57 : 3
(1976 ),
pp. 275–277 .
MR
0422544 Zbl
0343.26017 article
Abstract
BibTeX
@article {key0422544m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {An inequality for integrals},
JOURNAL = {Studia Math.},
FJOURNAL = {Studia Mathematica. Polska Akademia
Nauk. Instytut Matematyczny},
VOLUME = {57},
NUMBER = {3},
YEAR = {1976},
PAGES = {275--277},
URL = {http://matwbn.icm.edu.pl/ksiazki/sm/sm57/sm57120.pdf},
NOTE = {MR:0422544. Zbl:0343.26017.},
ISSN = {0039-3223},
}
[71]
A. P. Calderón :
Lecture notes on pseudo-differential operators and elliptic boundary value problems .
Cursos de Matemática 1 .
Instituto Argentino de Matemática (Buenos Aires ),
1976 .
MR
0460947 Zbl
0335.35082 book
BibTeX
@book {key0460947m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Lecture notes on pseudo-differential
operators and elliptic boundary value
problems},
SERIES = {Cursos de Matem\'atica},
NUMBER = {1},
PUBLISHER = {Instituto Argentino de Matem\'atica},
ADDRESS = {Buenos Aires},
YEAR = {1976},
PAGES = {89},
NOTE = {MR:0460947. Zbl:0335.35082.},
ISSN = {0326-291X},
}
[72]
A. P. Calderón and A. Torchinsky :
“Parabolic maximal functions associated with a distribution, II Adv. Math.
24 : 1
(April 1977 ),
pp. 101–171 .
Dedicated to the memory of Norman Levinson.
MR
0450888 Zbl
0355.46021 article
People
BibTeX
@article {key0450888m,
AUTHOR = {Calder\'on, A. P. and Torchinsky, A.},
TITLE = {Parabolic maximal functions associated
with a distribution, {II}},
JOURNAL = {Adv. Math.},
FJOURNAL = {Advances in Mathematics},
VOLUME = {24},
NUMBER = {1},
MONTH = {April},
YEAR = {1977},
PAGES = {101--171},
DOI = {10.1016/S0001-8708(77)80016-9},
NOTE = {Dedicated to the memory of Norman Levinson.
MR:0450888. Zbl:0355.46021.},
ISSN = {0001-8708},
}
[73]
A. P. Calderón :
“An atomic decomposition of distributions in parabolic \( H^p \) spaces Adv. Math.
25 : 3
(September 1977 ),
pp. 216–225 .
MR
0448066 Zbl
0379.46050 article
Abstract
BibTeX
The results of R. H. Latter on atomic decomposition are extended to distributions in parabolic \( H^p \) spaces with diagonalizable dilation groups. The method employed uses a decomposition of the function
\[ F(x,t) = f * \phi_t \]
associated with the distribution \( f \) , which also yields real and complex interpolation results for these spaces.
@article {key0448066m,
AUTHOR = {Calder\'on, Alberto P.},
TITLE = {An atomic decomposition of distributions
in parabolic \$H^p\$ spaces},
JOURNAL = {Adv. Math.},
FJOURNAL = {Advances in Mathematics},
VOLUME = {25},
NUMBER = {3},
MONTH = {September},
YEAR = {1977},
PAGES = {216--225},
DOI = {10.1016/0001-8708(77)90074-3},
NOTE = {MR:0448066. Zbl:0379.46050.},
ISSN = {0001-8708},
}
[74]
A. P. Calderón :
“Cauchy integrals on Lipschitz curves and related operators Proc. Natl. Acad. Sci. U.S.A.
74 : 4
(April 1977 ),
pp. 1324–1327 .
MR
0466568 Zbl
0373.44003 article
Abstract
BibTeX
In this note, we establish certain properties of the Cauchy integral on Lipschitz curves and prove the \( L^p \) -boundedness of some related operators. In particular, we obtain the recent results of R. R. Coifman and Y. Meyer [1976] on the continuity of the so-called commutator operators.
@article {key0466568m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Cauchy integrals on {L}ipschitz curves
and related operators},
JOURNAL = {Proc. Natl. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {74},
NUMBER = {4},
MONTH = {April},
YEAR = {1977},
PAGES = {1324--1327},
DOI = {10.1073/pnas.74.4.1324},
NOTE = {MR:0466568. Zbl:0373.44003.},
ISSN = {0027-8424},
}
[75]
A.-P. Calderón and A. Zygmund :
“On singular integrals with variable kernels Appl. Anal.
7 : 3
(1977–1978 ),
pp. 221–238 .
Dedicated to S. G. Mikhilin on the occasion of his 70th birthday.
MR
0511145 Zbl
0451.42012 article
People
BibTeX
@article {key0511145m,
AUTHOR = {Calder\'on, A.-P. and Zygmund, A.},
TITLE = {On singular integrals with variable
kernels},
JOURNAL = {Appl. Anal.},
FJOURNAL = {Applicable Analysis. An International
Journal},
VOLUME = {7},
NUMBER = {3},
YEAR = {1977--1978},
PAGES = {221--238},
DOI = {10.1080/00036817808839193},
NOTE = {Dedicated to S. G. Mikhilin on the occasion
of his 70th birthday. MR:0511145. Zbl:0451.42012.},
ISSN = {0003-6811},
}
[76]
A. P. Calderón, C. P. Calderon, E. Fabes, M. Jodeit, and N. M. Rivière :
“Applications of the Cauchy integral on Lipschitz curves Bull. Am. Math. Soc.
84 : 2
(March 1978 ),
pp. 287–290 .
MR
0460656 Zbl
0389.30025 article
People
BibTeX
@article {key0460656m,
AUTHOR = {Calder\'on, A. P. and Calderon, C. P.
and Fabes, E. and Jodeit, M. and Rivi\`ere,
N. M.},
TITLE = {Applications of the {C}auchy integral
on {L}ipschitz curves},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {84},
NUMBER = {2},
MONTH = {March},
YEAR = {1978},
PAGES = {287--290},
DOI = {10.1090/S0002-9904-1978-14478-4},
NOTE = {MR:0460656. Zbl:0389.30025.},
ISSN = {0002-9904},
}
[77]
A. P. Calderón :
“Correction to: ‘On an integral of Marcinkiewicz’ Studia Math.
62 : 1
(1978 ),
pp. 105 .
Correction to article published in Studia Math. 57 (1976)
MR
0493196 article
BibTeX
@article {key0493196m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Correction to: ``{O}n an integral of
{M}arcinkiewicz''},
JOURNAL = {Studia Math.},
FJOURNAL = {Studia Mathematica. Polska Akademia
Nauk. Instytut Matematyczny},
VOLUME = {62},
NUMBER = {1},
YEAR = {1978},
PAGES = {105},
URL = {http://matwbn.icm.edu.pl/ksiazki/sm/sm62/sm62111.pdf},
NOTE = {Correction to article published in \textit{Studia
Math.} \textbf{57} (1976). MR:0493196.},
ISSN = {0039-3223},
}
[78]
A. P. Calderón and R. Scott :
“Sobolev type inequalities for \( p > 0 \) Studia Math.
62 : 1
(1978 ),
pp. 75–92 .
MR
0487419 Zbl
0399.46031 article
Abstract
People
BibTeX
@article {key0487419m,
AUTHOR = {Calder\'on, Alberto P. and Scott, Ridgway},
TITLE = {Sobolev type inequalities for \$p>0\$},
JOURNAL = {Studia Math.},
FJOURNAL = {Studia Mathematica. Polska Akademia
Nauk. Instytut Matematyczny},
VOLUME = {62},
NUMBER = {1},
YEAR = {1978},
PAGES = {75--92},
URL = {http://matwbn.icm.edu.pl/ksiazki/sm/sm62/sm6218.pdf},
NOTE = {MR:0487419. Zbl:0399.46031.},
ISSN = {0039-3223},
}
[79]
A. González Domínguez :
“Dr. Alberto P. Calderón–Bôcher Prize 1979 ,”
Ciencia e Investigación
34
(November–December 1978 ),
pp. 221–223 .
article
People
BibTeX
@article {key54058976,
AUTHOR = {Gonz\'alez Dom\'{\i}nguez, Alberto},
TITLE = {Dr. {A}lberto {P}. {C}alder\'on -- {B}\^ocher
{P}rize 1979},
JOURNAL = {Ciencia e Investigaci\'on},
FJOURNAL = {Ciencia e Investigaci\'on},
VOLUME = {34},
MONTH = {November--December},
YEAR = {1978},
PAGES = {221--223},
ISSN = {1561-0861},
}
[80]
A.-P. Calderón and A. Zygmund :
“A note on singular integrals Studia Math.
65 : 1
(1979 ),
pp. 77–87 .
MR
554542 Zbl
0431.42007 article
Abstract
People
BibTeX
@article {key554542m,
AUTHOR = {Calder\'on, A.-P. and Zygmund, A.},
TITLE = {A note on singular integrals},
JOURNAL = {Studia Math.},
FJOURNAL = {Studia Mathematica. Polska Akademia
Nauk},
VOLUME = {65},
NUMBER = {1},
YEAR = {1979},
PAGES = {77--87},
URL = {http://matwbn.icm.edu.pl/ksiazki/sm/sm65/sm6517.pdf},
NOTE = {MR:554542. Zbl:0431.42007.},
ISSN = {0039-3223},
CODEN = {SMATAZ},
}
[81]
A. Calderón, E. Fabes, and Y. Sagher :
“Nestor M. Rivière: June 10, 1940–January 3, 1978 ,”
pp. vii–xvii
in
Harmonic analysis in Euclidean spaces
(Williamstown, MA, 10–28 July 1978 ),
part 1 .
Edited by G. L. Weiss and S. Wainger .
Proceedings of Symposia in Pure Mathematics 35 .
American Mathematical Society (Providence, RI ),
1979 .
MR
545234 Zbl
0409.01012 incollection
People
BibTeX
@incollection {key545234m,
AUTHOR = {Calder\'on, Alberto and Fabes, Eugene
and Sagher, Yoram},
TITLE = {Nestor {M}. {R}ivi\`ere: {J}une 10,
1940--{J}anuary 3, 1978},
BOOKTITLE = {Harmonic analysis in {E}uclidean spaces},
EDITOR = {Weiss, Guido L. and Wainger, Stephen},
VOLUME = {1},
SERIES = {Proceedings of Symposia in Pure Mathematics},
NUMBER = {35},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1979},
PAGES = {vii--xvii},
NOTE = {(Williamstown, MA, 10--28 July 1978).
MR:545234. Zbl:0409.01012.},
ISSN = {0082-0717},
ISBN = {9780821867945},
}
[82]
A. P. Calderón :
“Commutators, singular integrals on Lipschitz curves and applications 85–96
in
Proceedings of the International Congress of Mathematicians
(Helsinki, 15–23 August 1978 ),
vol. 1 .
Edited by O. Lehto .
University of Helsinki ,
1980 .
MR
562599 Zbl
0429.35077 incollection
Abstract
People
BibTeX
The topics discussed in this lecture had their origin in the theory of linear partial differential equations. In order to explain how the problem of the so-called commutators and that of the Cauchy integral on Lipschitz curves arose, I will recall and analyze some of the modern methods employed in the theory of linear partial differential equations, and in particular that of the pseudodifferential operators which became widely used in the last decade.
@incollection {key562599m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Commutators, singular integrals on {L}ipschitz
curves and applications},
BOOKTITLE = {Proceedings of the {I}nternational {C}ongress
of {M}athematicians},
EDITOR = {Lehto, Olli},
VOLUME = {1},
PUBLISHER = {University of Helsinki},
YEAR = {1980},
PAGES = {85--96},
URL = {http://www.mathunion.org/ICM/ICM1978.1/Main/icm1978.1.0085.0096.ocr.pdf},
NOTE = {(Helsinki, 15--23 August 1978). MR:562599.
Zbl:0429.35077.},
}
[83]
A. P. Calderón :
“On an inverse boundary value problem ,”
pp. 65–73
in
Seminar on numerical analysis and its applications to continuum physics
(Rio de Janeiro, 24–28 March 1980 ).
Coleção Atas 12 .
Sociedade Brasileira de Matemática (Rio de Janeiro ),
1980 .
Reprinted in Comput. Appl. Math. 25 :2–3 (2006)
MR
590275 incollection
BibTeX
@incollection {key590275m,
AUTHOR = {Calder\'on, Alberto P.},
TITLE = {On an inverse boundary value problem},
BOOKTITLE = {Seminar on numerical analysis and its
applications to continuum physics},
SERIES = {Cole\c{c}\~{a}o Atas},
NUMBER = {12},
PUBLISHER = {Sociedade Brasileira de Matem\'atica},
ADDRESS = {Rio de Janeiro},
YEAR = {1980},
PAGES = {65--73},
NOTE = {(Rio de Janeiro, 24--28 March 1980).
Reprinted in \textit{Comput. Appl. Math.}
\textbf{25}:2--3 (2006). MR:590275.},
}
[84]
J. Álvarez Alonso and A. P. Calderón :
“Functional calculi for pseudodifferential operators, I ,”
pp. 1–61
in
Fourier analysis
(El Escorial, Spain, 17–23 June 1979 ).
Edited by I. Peral and M. de Guzmán .
Asociación Matemática Española (Madrid ),
1980 .
Part II was published in Studies in applied mathematics: {A volume dedicated to {I}rving {S}egal} (1983)
MR
582249 Zbl
0471.47030 incollection
People
BibTeX
@incollection {key582249m,
AUTHOR = {{\'A}lvarez Alonso, Josefina and Calder\'on,
A. P.},
TITLE = {Functional calculi for pseudodifferential
operators, {I}},
BOOKTITLE = {Fourier analysis},
EDITOR = {Peral, Ireneo and de Guzm\'an, Miguel},
PUBLISHER = {Asociaci\'on Matem\'atica Espa\~nola},
ADDRESS = {Madrid},
YEAR = {1980},
PAGES = {1--61},
NOTE = {(El Escorial, Spain, 17--23 June 1979).
Part II was published in \textit{Studies
in applied mathematics: {A} volume dedicated
to {I}rving {S}egal} (1983). MR:582249.
Zbl:0471.47030.},
ISBN = {9788430021727},
}
[85]
Conference on harmonic analysis in honor of Antoni Zygmund
(Chicago, 23–28 March 1981 ),
vol. 1 and 2 .
Edited by W. Beckner, A. P. Calderón, R. Fefferman, and P. W. Jones .
Wadsworth Mathematics Series .
Wadsworth (Belmont, CA ),
1983 .
MR
0730053 Zbl
0493.00009 book
People
BibTeX
@book {keyMR0730053m,
TITLE = {Conference on harmonic analysis in honor
of {A}ntoni {Z}ygmund},
EDITOR = {Beckner, William and Calder\'on, Albert
P. and Fefferman, Robert and Jones,
Peter W.},
VOLUME = {1 and 2},
SERIES = {Wadsworth Mathematics Series},
PUBLISHER = {Wadsworth},
ADDRESS = {Belmont, CA},
YEAR = {1983},
PAGES = {xv+837},
NOTE = {(Chicago, 23--28 March 1981). MR:MR0730053.
Zbl:0493.00009.},
ISBN = {9780534980405},
}
[86]
A. P. Calderón :
“Antoni Zygmund ,”
pp. xiii–xv
in
Conference on harmonic analysis in honor of Antoni Zygmund
(Chicago, IL, 23–28 March 1981 ),
vol. 2 .
Edited by W. Beckner, A. P. Calderón, R. Fefferman, and P. W. Jones .
Wadsworth Mathematics Series .
Wadsworth (Belmont, CA ),
1983 .
MR
730054 Zbl
0532.42001 incollection
People
BibTeX
@incollection {key730054m,
AUTHOR = {Calder\'on, Alberto P.},
TITLE = {Antoni {Z}ygmund},
BOOKTITLE = {Conference on harmonic analysis in honor
of {A}ntoni {Z}ygmund},
EDITOR = {Beckner, William and Calder\'on, Alberto
P. and Fefferman, Robert and Jones,
Peter W.},
VOLUME = {2},
SERIES = {Wadsworth Mathematics Series},
PUBLISHER = {Wadsworth},
ADDRESS = {Belmont, CA},
YEAR = {1983},
PAGES = {xiii--xv},
NOTE = {(Chicago, IL, 23--28 March 1981). MR:730054.
Zbl:0532.42001.},
ISBN = {9780534980412},
}
[87]
A. P. Calderón :
“On the Radon transform and some of its generalizations ,”
pp. 673–689
in
Conference on harmonic analysis in honor of Antoni Zygmund
(Chicago, IL, 23–28 March 1981 ),
vol. 2 .
Edited by W. Beckner, A. P. Calderón, R. Fefferman, and P. W. Jones .
Wadsworth Mathematics Series .
Wadsworth (Belmont, CA ),
1983 .
MR
730101 Zbl
0508.43004 incollection
People
BibTeX
@incollection {key730101m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {On the {R}adon transform and some of
its generalizations},
BOOKTITLE = {Conference on harmonic analysis in honor
of {A}ntoni {Z}ygmund},
EDITOR = {Beckner, William and Calder\'on, Alberto
P. and Fefferman, Robert and Jones,
Peter W.},
VOLUME = {2},
SERIES = {Wadsworth Mathematics Series},
PUBLISHER = {Wadsworth},
ADDRESS = {Belmont, CA},
YEAR = {1983},
PAGES = {673--689},
NOTE = {(Chicago, IL, 23--28 March 1981). MR:730101.
Zbl:0508.43004.},
ISBN = {9780534980412},
}
[88]
Conference on harmonic analysis in honor of Antoni Zygmund
(Chicago, IL, 23–28 March 1981 ),
vol. 2 .
Edited by W. Beckner, A. P. Calderón, R. Fefferman, and P. W. Jones .
Wadsworth Mathematics Series .
Wadsworth (Belmont, CA ),
1983 .
book
People
BibTeX
@book {key68897695,
TITLE = {Conference on harmonic analysis in honor
of {A}ntoni {Z}ygmund},
EDITOR = {Beckner, William and Calder\'on, Alberto
P. and Fefferman, Robert and Jones,
Peter W.},
VOLUME = {2},
SERIES = {Wadsworth Mathematics Series},
PUBLISHER = {Wadsworth},
ADDRESS = {Belmont, CA},
YEAR = {1983},
PAGES = {850},
NOTE = {(Chicago, IL, 23--28 March 1981).},
ISBN = {9780534980412},
}
[89]
J. D. Álvarez Alonso and A. P. Calderón :
“Functional calculi for pseudodifferential operators, II ,”
pp. 27–72
in
Studies in applied mathematics: A volume dedicated to Irving Segal ,
vol. 8 .
Edited by V. Guillemin .
Advances in Mathematics: Supplementary Studies .
Academic Press (New York ),
1983 .
Part I was published in Fourier analysis (1980)
MR
759905 Zbl
0515.47026 incollection
People
BibTeX
@incollection {key759905m,
AUTHOR = {{\'A}lvarez Alonso, J. D. and Calder\'on,
Alberto P.},
TITLE = {Functional calculi for pseudodifferential
operators, {II}},
BOOKTITLE = {Studies in applied mathematics: {A}
volume dedicated to {I}rving {S}egal},
EDITOR = {Guillemin, V.},
VOLUME = {8},
SERIES = {Advances in Mathematics: Supplementary
Studies},
PUBLISHER = {Academic Press},
ADDRESS = {New York},
YEAR = {1983},
PAGES = {27--72},
NOTE = {Part I was published in \textit{Fourier
analysis} (1980). MR:759905. Zbl:0515.47026.},
ISBN = {9780123054807},
}
[90]
A. P. Calderón and O. N. Capri :
“On the convergence in \( L^1 \) of singular integrals Studia Math.
78 : 3
(1984 ),
pp. 321–327 .
MR
782669 Zbl
0488.42017 article
Abstract
People
BibTeX
It is shown that if a singular integral such as in [Benedek, Calderón and Panzone 1962] acting on a function in \( L^1 \) is in \( L^1 \) , then the truncated operator converges to its limit in \( L^1 \) .
@article {key782669m,
AUTHOR = {Calder\'on, Alberto P. and Capri, Osvaldo
N.},
TITLE = {On the convergence in \$L^1\$ of singular
integrals},
JOURNAL = {Studia Math.},
FJOURNAL = {Studia Mathematica. Polska Akademia
Nauk. Instytut Matematyczny},
VOLUME = {78},
NUMBER = {3},
YEAR = {1984},
PAGES = {321--327},
URL = {http://matwbn.icm.edu.pl/ksiazki/sm/sm78/sm78128.pdf},
NOTE = {MR:782669. Zbl:0488.42017.},
ISSN = {0039-3223},
CODEN = {SMATAZ},
}
[91]
“Alberto Calderón ,”
C. R. Acad. Sci. Sér. Gén. Vie Sci.
1 : 6
(1984 ),
pp. 514–515 .
MR
0788209 article
BibTeX
@article {key0788209m,
TITLE = {Alberto Calder\'on},
JOURNAL = {C. R. Acad. Sci. S\'er. G\'en. Vie Sci.},
FJOURNAL = {Comptes Rendus de l'Acad\'emie des Sciences.
S\'erie G\'en\'erale. La Vie des Sciences},
VOLUME = {1},
NUMBER = {6},
YEAR = {1984},
PAGES = {514--515},
NOTE = {MR:0788209.},
ISSN = {0002-3302},
}
[92]
A. P. Calderón :
“Boundary value problems for the Laplace equation in Lipschitzian domains 33–48
in
Recent progress in Fourier analysis ,
vol. 111 .
Edited by I. Peral and J.-L. Rubio de Francia .
North-Holland Mathematics Studies .
North-Holland (Amsterdam ),
1985 .
MR
848140 Zbl
0608.31001 incollection
People
BibTeX
@incollection {key848140m,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Boundary value problems for the {L}aplace
equation in {L}ipschitzian domains},
BOOKTITLE = {Recent progress in {F}ourier analysis},
EDITOR = {Peral, I. and Rubio de Francia, J.-L.},
VOLUME = {111},
SERIES = {North-Holland Mathematics Studies},
PUBLISHER = {North-Holland},
ADDRESS = {Amsterdam},
YEAR = {1985},
PAGES = {33--48},
DOI = {10.1016/S0304-0208(08)70278-0},
NOTE = {MR:848140. Zbl:0608.31001.},
ISSN = {0304-0208},
ISBN = {9780080872223},
}
[93]
A. P. Calderón :
“Reflexiones sobre el aprendizaje y enseñanza de la Matemática Reflections on learning and teaching mathematics ],
Rev. Educ. Mat.
3 : 1
(1987 ),
pp. 3–13 .
Reprinted in Gac. R. Soc. Mat. Esp. 1 :1 (1998)
article
BibTeX
@article {key26357774,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Reflexiones sobre el aprendizaje y ense\~{n}anza
de la Matem\'atica [Reflections on learning
and teaching mathematics]},
JOURNAL = {Rev. Educ. Mat.},
FJOURNAL = {Revista de Educaci\'on Matem\'atica},
VOLUME = {3},
NUMBER = {1},
YEAR = {1987},
PAGES = {3--13},
URL = {http://www.revistas.unc.edu.ar/index.php/REM/article/view/11230/11778},
NOTE = {Reprinted in \textit{Gac. R. Soc. Mat.
Esp.} \textbf{1}:1 (1998).},
ISSN = {0326-8780},
}
[94]
A. P. Calderón :
“Presentación del Dr. Eduardo H. Zarantonello como Académico Correspondiente en la ciudad de Mendoza ”
[Presentation of Dr. Eduardo Zarantonello as Academic Correspondent in the city of Mendoza ],
Anales Acad. Nac. Ciencias Exac. Fís. y Nat.
40
(1988 ),
pp. 95–96 .
article
People
BibTeX
Eduardo Héctor Zarantonello
Related
@article {key88118244,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Presentaci\'on del {D}r. {E}duardo {H}.
{Z}arantonello como {A}cad\'emico {C}orrespondiente
en la ciudad de {M}endoza [Presentation
of {D}r. {E}duardo {Z}arantonello as
{A}cademic {C}orrespondent in the city
of {M}endoza]},
JOURNAL = {Anales Acad. Nac. Ciencias Exac. F\'{\i}s.
y Nat.},
FJOURNAL = {Anales de la Academia Nacional de Cienceas
Exacta, F\'{\i}sicas y Naturales},
VOLUME = {40},
YEAR = {1988},
PAGES = {95--96},
ISSN = {0365-1185},
}
[95]
J. E. Santos, J. Douglas, Jr., and A. P. Calderón :
“Finite element methods for a composite model in elastodynamics SIAM J. Numer. Anal.
25 : 3
(1988 ),
pp. 513–532 .
MR
942205 Zbl
0684.73034 article
Abstract
People
BibTeX
The propagation of waves through a composite isotropic nonhomogeneous elastic system \( \Omega \) consisting of an elastic solid \( \Omega_s \) with an imbedded fluid-saturated porous medium \( \Omega_p \) is analyzed. The linear elastodynamic equation for \( \Omega_s \) and Biot’s low-frequency dynamic equations for \( \Omega_p \) are chosen to describe the propagation, with appropriate boundary conditions at the interface between the media and along the artificial boundaries of the model.
First the existence and uniqueness of the solution are analyzed and then the continuous and discrete-time Galerkin procedures for obtaining approximate solutions are defined.
Standard finite element subspaces of \( H^1(\Omega) \) are used to approximate the displacement vector components for the solid part of \( \Omega \) , while mixed finite element subspaces of \( H(\operatorname{div},\Omega_p) \) are employed to approximate the vector displacement for \( \Omega_p \) . Convergence of optimal order is derived for the methods under certain smoothness assumptions for the solution of the differential problem.
@article {key942205m,
AUTHOR = {Santos, Juan Enrique and Douglas, Jr.,
Jim and Calder\'on, Alberto Pedro},
TITLE = {Finite element methods for a composite
model in elastodynamics},
JOURNAL = {SIAM J. Numer. Anal.},
FJOURNAL = {SIAM Journal on Numerical Analysis},
VOLUME = {25},
NUMBER = {3},
YEAR = {1988},
PAGES = {513--532},
DOI = {10.1137/0725033},
NOTE = {MR:942205. Zbl:0684.73034.},
ISSN = {0036-1429},
CODEN = {SJNAAM},
}
[96]
A. P. Calderón :
“Introduction of Professor Mischa Cotlar to the National Academy of Exact Sciences of Argentina ,”
pp. xix–xx
in
Analysis and partial differential equations ,
vol. 122 .
Edited by C. Sadosky .
Lecture Notes in Pure and Applied Mathematics .
Dekker (New York ),
1989 .
English translation of original Spanish article published in Anales Acad. Nac. Ciencias Exac. Fís. y Nat. 41 (1989)
MR
1044777 incollection
People
BibTeX
@incollection {key1044777m,
AUTHOR = {Calder\'on, Alberto P.},
TITLE = {Introduction of {P}rofessor {M}ischa
{C}otlar to the {N}ational {A}cademy
of {E}xact {S}ciences of {A}rgentina},
BOOKTITLE = {Analysis and partial differential equations},
EDITOR = {Sadosky, Cora},
VOLUME = {122},
SERIES = {Lecture Notes in Pure and Applied Mathematics},
PUBLISHER = {Dekker},
ADDRESS = {New York},
YEAR = {1989},
PAGES = {xix--xx},
NOTE = {English translation of original Spanish
article published in \textit{Anales
Acad. Nac. Ciencias Exac. F\'{\i}s.
y Nat.} \textbf{41} (1989). MR:1044777.},
ISSN = {0075-8469},
ISBN = {9780849306532},
}
[97]
A. P. Calderón :
“Presentación del Dr. Mischa Cotlar como Académico Correspondiente en Caracas ”
[Presentation of Dr. Misha Cotlar as Academic Correspondent in Caracas ],
Anales Acad. Nac. Ciencias Exac. Fís. y Nat.
41
(1989 ),
pp. 37–38 .
An English version of this was published in Analysis and partial differential equations (1989)
article
People
BibTeX
@article {key11247688,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Presentaci\'on del {D}r. {M}ischa {C}otlar
como {A}cad\'emico {C}orrespondiente
en Caracas [Presentation of {D}r. {M}isha
{C}otlar as {A}cademic {C}orrespondent
in {C}aracas]},
JOURNAL = {Anales Acad. Nac. Ciencias Exac. F\'{\i}s.
y Nat.},
FJOURNAL = {Anales de la Academia Nacional de Cienceas
Exacta, F\'{\i}sicas y Naturales},
VOLUME = {41},
YEAR = {1989},
PAGES = {37--38},
NOTE = {An English version of this was published
in \textit{Analysis and partial differential
equations} (1989).},
ISSN = {0365-1185},
}
[98]
A. P. Calderón :
“Presentación del Dr. Carlos Segovia Fernández como Académico Titular ”
[Presentation of Dr. Carlos Segovia Fernández as Member of the Academy ],
Anales Acad. Nac. Ciencias Exac. Fís. y Nat.
42
(1990 ),
pp. 29–30 .
article
People
BibTeX
@article {key24968820,
AUTHOR = {Calder\'on, A. P.},
TITLE = {Presentaci\'on del {D}r. {C}arlos {S}egovia
{F}ern\'andez como {A}cad\'emico {T}itular
[Presentation of {D}r. {C}arlos {S}egovia
{F}ern\'andez as {M}ember of the {A}cademy]},
JOURNAL = {Anales Acad. Nac. Ciencias Exac. F\'{\i}s.
y Nat.},
FJOURNAL = {Anales de la Academia Nacional de Cienceas
Exacta, F\'{\i}sicas y Naturales},
VOLUME = {42},
YEAR = {1990},
PAGES = {29--30},
ISSN = {0365-1185},
}
[99]
A. P. Calderón and Y. Sagher :
“The Hilbert transform of the Gaussian ,”
pp. 109–112
in
Almost everywhere convergence II
(Evanston, IL, 16–20 October 1989 ).
Edited by A. Bellow and R. L. Jones .
Academic Press (Boston, MA ),
1991 .
Dedicated to the memory of N. M. Rivière.
MR
1131786 Zbl
0743.44004 incollection
Abstract
People
BibTeX
In this short note we calculate the Hilbert transform of the Gaussian. The problem was first mentioned to one of us some twenty years ago, by N. M. Rivière. As it turns out, the solution is very natural, leading to a well known function. We will give two proofs of the result, the second much shorter than the first. On the other hand the first proof yields some additional results. It also suggests a connection between the Hilbert transform and the one dimensional heat equation. For some applicastion sof this connection see [Kochneff, Sagher and Zhou 1992], where the Hilbert transforms of the Hermite functions \( H_n(x)\,\mathcal{G}(x) \) are also calculated.
@incollection {key1131786m,
AUTHOR = {Calder\'on, A. P. and Sagher, Y.},
TITLE = {The {H}ilbert transform of the {G}aussian},
BOOKTITLE = {Almost everywhere convergence {II}},
EDITOR = {Bellow, Alexandra and Jones, Roger L.},
PUBLISHER = {Academic Press},
ADDRESS = {Boston, MA},
YEAR = {1991},
PAGES = {109--112},
NOTE = {(Evanston, IL, 16--20 October 1989).
Dedicated to the memory of N. M. Rivi\`ere.
MR:1131786. Zbl:0743.44004.},
ISBN = {9781483265926},
}
[100]
A. P. Calderón and E. M. Stein :
“Antoni Zygmund: 1900–1992 ,”
Notices Am. Math. Soc.
39 : 8
(1992 ),
pp. 848–849 .
MR
1182969 Zbl
1194.01074 article
People
BibTeX
@article {key1182969m,
AUTHOR = {Calder\'on, A. P. and Stein, Elias M.},
TITLE = {Antoni {Z}ygmund: 1900--1992},
JOURNAL = {Notices Am. Math. Soc.},
FJOURNAL = {Notices of the American Mathematical
Society},
VOLUME = {39},
NUMBER = {8},
YEAR = {1992},
PAGES = {848--849},
NOTE = {MR:1182969. Zbl:1194.01074.},
ISSN = {0002-9920},
}
[101]
R. W. Beals, R. R. Coifman, and P. W. Jones :
“Alberto P. Calderón receives National Medal of Science ,”
Notices Am. Math. Soc.
39 : 4
(1992 ),
pp. 283–285 .
article
People
BibTeX
@article {key37867655,
AUTHOR = {Beals, R. W. and Coifman, R. R. and
Jones, P. W.},
TITLE = {Alberto P. Calder\'on receives {N}ational
{M}edal of {S}cience},
JOURNAL = {Notices Am. Math. Soc.},
FJOURNAL = {Notices of the American Mathematical
Society},
VOLUME = {39},
NUMBER = {4},
YEAR = {1992},
PAGES = {283--285},
ISSN = {0002-9920},
}
[102]
A. Bellow, A. P. Calderón, and U. Krengel :
“Hopf’s ergodic theorem for particles with different velocities and the ‘strong sweeping out property’ Can. Math. Bull.
38 : 1
(1995 ),
pp. 11–15 .
MR
1319895 Zbl
0821.28009 article
Abstract
People
BibTeX
In an earlier paper we provided a counterexample to an old conjecture of Hopf. In this note we show that the “strong sweeping out property” obtains for the Hopf operators (\( T_t \) ) both when \( t \to +\infty \) and when \( t \to 0+ \) , that is a.e. convergence fails in the worst possible way.
@article {key1319895m,
AUTHOR = {Bellow, A. and Calder\'on, A. P. and
Krengel, U.},
TITLE = {Hopf's ergodic theorem for particles
with different velocities and the ``strong
sweeping out property''},
JOURNAL = {Can. Math. Bull.},
FJOURNAL = {Canadian Mathematical Bulletin},
VOLUME = {38},
NUMBER = {1},
YEAR = {1995},
PAGES = {11--15},
DOI = {10.4153/CMB-1995-002-0},
NOTE = {MR:1319895. Zbl:0821.28009.},
ISSN = {0008-4395},
CODEN = {CMBUA3},
}
[103]
A. Carbery :
“Harmonic analysis of the Calderón–Zygmund school, 1970–1993 ,”
Bull. London Math. Soc.
30 : 1
(1998 ),
pp. 11–23 .
MR
1479031 article
People
BibTeX
@article {key1479031m,
AUTHOR = {Carbery, A.},
TITLE = {Harmonic analysis of the {C}alder\'on--{Z}ygmund
school, 1970--1993},
JOURNAL = {Bull. London Math. Soc.},
FJOURNAL = {Bulletin of the London Mathematical
Society},
VOLUME = {30},
NUMBER = {1},
YEAR = {1998},
PAGES = {11--23},
NOTE = {MR:1479031.},
}
[104]
M. Christ, C. E. Kenig, C. Sadosky, and G. Weiss :
“Alberto Pedro Calderón (1920–1998) Notices Am. Math. Soc.
45 : 9
(September 1998 ),
pp. 1148–1153 .
MR
1640167 Zbl
0973.01072 article
People
BibTeX
@article {key1640167m,
AUTHOR = {Christ, Michael and Kenig, Carlos E.
and Sadosky, Cora and Weiss, Guido},
TITLE = {Alberto {P}edro {C}alder\'on (1920--1998)},
JOURNAL = {Notices Am. Math. Soc.},
FJOURNAL = {Notices of the American Mathematical
Society},
VOLUME = {45},
NUMBER = {9},
MONTH = {September},
YEAR = {1998},
PAGES = {1148--1153},
URL = {http://www.ams.org/notices/199809/mem-calderon.pdf},
NOTE = {MR:1640167. Zbl:0973.01072.},
ISSN = {0002-9920},
}
[105]
H. B. Noble :
“Obituary: Alberto Calderón, 77, pioneer of mathematical analysis New York Times
(20 April 1998 ).
article
People
BibTeX
@article {key76682371,
AUTHOR = {Noble, Holcomb B.},
TITLE = {Obituary: {A}lberto {C}alder\'on, 77,
pioneer of mathematical analysis},
JOURNAL = {New York Times},
FJOURNAL = {The New York Times},
MONTH = {20 April},
YEAR = {1998},
URL = {http://www.nytimes.com/1998/04/20/us/alberto-calderon-77-pioneer-of-mathematical-analysis.html},
ISSN = {0362-4331},
}
[106]
A. P. Calderón :
“Reflexiones sobre el aprendizaje y enseñanza de la matemática Reflections on learning and teaching mathematics ],
Gac. R. Soc. Mat. Esp.
1 : 1
(January–April 1998 ),
pp. 80–88 .
Reprinted from Rev. Educ. Mat. 3 :1 (1987)
MR
1647672 article
BibTeX
@article {key1647672m,
AUTHOR = {Calder\'on, Alberto P.},
TITLE = {Reflexiones sobre el aprendizaje y ense\~{n}anza
de la matem\'atica [Reflections on learning
and teaching mathematics]},
JOURNAL = {Gac. R. Soc. Mat. Esp.},
FJOURNAL = {La Gaceta de la Real Sociedad Matem\'atica
Espa\~nola},
VOLUME = {1},
NUMBER = {1},
MONTH = {January--April},
YEAR = {1998},
PAGES = {80--88},
URL = {http://gaceta.rsme.es/english/abrir.php?id=304},
NOTE = {Reprinted from \textit{Rev. Educ. Mat.}
\textbf{3}:1 (1987). MR:1647672.},
ISSN = {1138-8927},
}
[107]
A. Carbery :
“Obituary: Alberto Calderón: Mathematics applied ,”
Guardian
(May 1998 ).
article
People
BibTeX
@article {key31500549,
AUTHOR = {Carbery, A.},
TITLE = {Obituary: {A}lberto {C}alder\'on: {M}athematics
applied},
JOURNAL = {Guardian},
FJOURNAL = {The Guardian},
MONTH = {May},
YEAR = {1998},
ISSN = {0261-3077},
}
[108]
“Obituary: Alberto Calderón Univ. Chicago Chronicle
17 : 15
(30 April 1998 ).
article
BibTeX
@article {key99820700,
TITLE = {Obituary: {A}lberto {C}alder\'on},
JOURNAL = {Univ. Chicago Chronicle},
FJOURNAL = {The University of Chicago Chronicle},
VOLUME = {17},
NUMBER = {15},
MONTH = {30 April},
YEAR = {1998},
URL = {http://chronicle.uchicago.edu/980430/calderon.shtml},
ISSN = {1095-1237},
}
[109]
C. Segovia Fernández :
“Alberto Pedro Calderón. Mathematician Rev. Un. Mat. Argentina
41 : 3
(1999 ),
pp. 129–140 .
MR
1763267 Zbl
0963.01015 article
People
BibTeX
@article {key1763267m,
AUTHOR = {Segovia Fern\'andez, Carlos},
TITLE = {Alberto {P}edro {C}alder\'on. {M}athematician},
JOURNAL = {Rev. Un. Mat. Argentina},
FJOURNAL = {Revista de la Uni\'on Matem\'atica Argentina},
VOLUME = {41},
NUMBER = {3},
YEAR = {1999},
PAGES = {129--140},
URL = {http://inmabb.criba.edu.ar/revuma/pdf/v41n3/v41n3a14.pdf},
NOTE = {MR:1763267. Zbl:0963.01015.},
ISSN = {0041-6932},
}
[110]
Harmonic analysis and partial differential equations: Essays in honor of Alberto P. Calderón
(Chicago, IL, February 1996 ).
Edited by M. Christ, C. E. Kenig, and C. Sadosky .
Chicago Lectures in Mathematics .
University of Chicago Press ,
1999 .
Essays in honor of Alberto P. Calderón’s 75th birthday.
MR
1731192 Zbl
0932.00088 book
People
BibTeX
@book {key1731192m,
TITLE = {Harmonic analysis and partial differential
equations: {E}ssays in honor of {A}lberto
{P}. {C}alder\'on},
EDITOR = {Christ, Michael and Kenig, Carlos E.
and Sadosky, Cora},
SERIES = {Chicago Lectures in Mathematics},
PUBLISHER = {University of Chicago Press},
YEAR = {1999},
PAGES = {xvi+355},
NOTE = {(Chicago, IL, February 1996). Essays
in honor of Alberto P. Calder\'on's
75th birthday. MR:1731192. Zbl:0932.00088.},
ISBN = {9780226104553},
}
[111]
A. Bellow and A. P. Calderón :
“A weak-type inequality for convolution products ,”
pp. 41–48
in
Harmonic analysis and partial differential equations: Essays in honor of Alberto P. Calderón
(Chicago, IL, February 1996 ).
Edited by M. Christ, C. E. Kenig, and C. Sadosky .
Chicago Lectures in Mathematics .
University of Chicago Press ,
1999 .
MR
1743854 Zbl
0960.28011 incollection
People
BibTeX
@incollection {key1743854m,
AUTHOR = {Bellow, Alexandra and Calder\'on, Alberto
P.},
TITLE = {A weak-type inequality for convolution
products},
BOOKTITLE = {Harmonic analysis and partial differential
equations: {E}ssays in honor of {A}lberto
{P}. {C}alder\'on},
EDITOR = {Christ, Michael and Kenig, Carlos E.
and Sadosky, Cora},
SERIES = {Chicago Lectures in Mathematics},
PUBLISHER = {University of Chicago Press},
YEAR = {1999},
PAGES = {41--48},
NOTE = {(Chicago, IL, February 1996). MR:1743854.
Zbl:0960.28011.},
ISBN = {9780226104553},
}
[112]
M. de Guzmán :
“Alberto P. Calderón (1920–1998). Algunos recuerdos de Chicago ”
[Alberto Calderón (1920–1998). Some reminiscences of Chicago ],
Cubo Mat. Educ.
2
(2000 ),
pp. 12–16 .
MR
1957365 Zbl
1067.01570 article
People
BibTeX
@article {key1957365m,
AUTHOR = {de Guzm\'an, Miguel},
TITLE = {Alberto {P}. {C}alder\'on (1920--1998).
{A}lgunos recuerdos de {C}hicago [Alberto
Calder\'on (1920--1998). {S}ome reminiscences
of {C}hicago]},
JOURNAL = {Cubo Mat. Educ.},
FJOURNAL = {Cubo Matem\'atica Educacional},
VOLUME = {2},
YEAR = {2000},
PAGES = {12--16},
NOTE = {MR:1957365. Zbl:1067.01570.},
ISSN = {0716-7776},
}
[113]
A. P. Calderon and C. P. Calderon :
“A representation formula and its applications to singular integrals Indiana Univ. Math. J.
49 : 1
(2000 ),
pp. 1–5 .
MR
1777040 Zbl
1031.42016 article
Abstract
BibTeX
@article {key1777040m,
AUTHOR = {Calderon, A. P. and Calderon, C. P.},
TITLE = {A representation formula and its applications
to singular integrals},
JOURNAL = {Indiana Univ. Math. J.},
FJOURNAL = {Indiana University Mathematics Journal},
VOLUME = {49},
NUMBER = {1},
YEAR = {2000},
PAGES = {1--5},
DOI = {10.1512/iumj.2000.49.1943},
NOTE = {MR:1777040. Zbl:1031.42016.},
ISSN = {0022-2518},
CODEN = {IUMJAB},
}
[114]
A. P. Calderón :
“On an inverse boundary value problem 133–138
in
Seminar on inverse problems and applications
(Rio de Janeiro, 21–24 March 2006 ),
published as Comput. Appl. Math.
25 : 2–3 .
Issue edited by G. Perla Menzala and G. Uhlmann .
2006 .
Reprinted from Seminar on numerical analysis and its applications to continuum physics (1980)
MR
2321646 Zbl
1182.35230 incollection
People
BibTeX
@article {key2321646m,
AUTHOR = {Calder\'on, Alberto P.},
TITLE = {On an inverse boundary value problem},
JOURNAL = {Comput. Appl. Math.},
FJOURNAL = {Computational \& Applied Mathematics},
VOLUME = {25},
NUMBER = {2--3},
YEAR = {2006},
PAGES = {133--138},
DOI = {10.1590/S0101-82052006000200002},
NOTE = {\textit{Seminar on inverse problems
and applications} (Rio de Janeiro, 21--24
March 2006). Issue edited by G. Perla
Menzala and G. Uhlmann.
Reprinted from \textit{Seminar on numerical
analysis and its applications to continuum
physics} (1980). MR:2321646. Zbl:1182.35230.},
ISSN = {0101-8205},
}
[115]
Y. Meyer :
“Complex analysis and operator theory in Alberto Calderón’s work ,”
pp. 593–606
in
Selected papers of Alberto P. Calderón .
Edited by A. Bellow, C. E. Kenig, and P. Malliavin .
American Mathematical Society (Providence, RI ),
2008 .
MR
2435338 incollection
People
BibTeX
@incollection {key2435338m,
AUTHOR = {Meyer, Yves},
TITLE = {Complex analysis and operator theory
in {A}lberto {C}alder\'on's work},
BOOKTITLE = {Selected papers of {A}lberto {P}. {C}alder\'on},
EDITOR = {Bellow, Alexandra and Kenig, Carlos
E. and Malliavin, Paul},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {2008},
PAGES = {593--606},
NOTE = {MR:2435338.},
ISBN = {9780821842973},
}
[116]
M. Christ, C. E. Kenig, and C. Sadosky :
“Alberto P. Calderón the mathematician, his life and works ,”
pp. xv–xx
in
Selected papers of Alberto P. Calderón .
Edited by A. Bellow, C. E. Kenig, and P. Malliavin .
American Mathematical Society (Providence, RI ),
2008 .
MR
2435330 incollection
People
BibTeX
@incollection {key2435330m,
AUTHOR = {Christ, Michael and Kenig, Carlos E.
and Sadosky, Cora},
TITLE = {Alberto {P}. {C}alder\'on the mathematician,
his life and works},
BOOKTITLE = {Selected papers of {A}lberto {P}. {C}alder\'on},
EDITOR = {Bellow, Alexandra and Kenig, Carlos
E. and Malliavin, Paul},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {2008},
PAGES = {xv--xx},
NOTE = {MR:2435330.},
ISBN = {9780821842973},
}
[117]
A. P. Calderón :
Selected papers of Alberto P. Calderón .
Edited by A. Bellow, C. E. Kenig, and P. Malliavin .
American Mathematical Society (Providence, RI ),
2008 .
with commentary.
MR
2435328 Zbl
1140.01021 book
People
BibTeX
@book {key2435328m,
AUTHOR = {Calder\'on, Alberto P.},
TITLE = {Selected papers of {A}lberto {P}. {C}alder\'on},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {2008},
PAGES = {xiv+639},
NOTE = {Edited by A. Bellow, C. E. Kenig,
and P. Malliavin. with commentary.
MR:2435328. Zbl:1140.01021.},
ISBN = {9780821842973},
}
[118]
Selected papers based on the presentations at the 10th “Encuentro Nacional de Analistas Alberto P. Calderón”
(Cordoba, Spain, 25–28 August 2010 ),
published as Rev. Un. Mat. Argentina
52 : 2 .
Issue edited by C. Cabrelli and E. Harboure .
2011 .
Zbl
1246.46002 book
People
BibTeX
Carlos Alberto Cabrelli
Related
Eleonor Ofelia Harboure de Aguilera
Related
@book {key1246.46002z,
TITLE = {Selected papers based on the presentations
at the 10th ``{E}ncuentro {N}acional
de {A}nalistas {A}lberto {P}. {C}alder\'on''},
EDITOR = {Cabrelli, Carlos and Harboure, Eleonor},
YEAR = {2011},
PAGES = {113},
NOTE = {(Cordoba, Spain, 25--28 August 2010).
Published as \textit{Rev. Un. Mat. Argentina}
\textbf{52}:2. Zbl:1246.46002.},
ISSN = {0041-6932},
}
