A. Zygmund :
“Une remarque sur un théorème de M. Kaczmarz ”
[A remark on a theorem of M. Kaczmarz ],
Math. Z.
25 : 1
(1926 ),
pp. 297–298 .
MR
1544811
JFM
52.0278.01
article
BibTeX
@article {key1544811m,
AUTHOR = {Zygmund, A.},
TITLE = {Une remarque sur un th\'eor\`eme de
{M}. {K}aczmarz [A remark on a theorem
of {M}. {K}aczmarz]},
JOURNAL = {Math. Z.},
FJOURNAL = {Mathematische Zeitschrift},
VOLUME = {25},
NUMBER = {1},
YEAR = {1926},
PAGES = {297--298},
DOI = {10.1007/BF01283839},
NOTE = {MR:1544811. JFM:52.0278.01.},
ISSN = {0025-5874},
CODEN = {MAZEAX},
}
A. Zygmund :
“Sur l’application de la première moyenne arithmétique dans la théorie des séries de fonctions orthogonales ”
[On the application of the first arithmetic mean to the theory of series of orthogonal functions ],
Fundam. Math.
10
(1927 ),
pp. 356–362 .
JFM
53.0267.04
article
BibTeX
@article {key53.0267.04j,
AUTHOR = {Zygmund, A.},
TITLE = {Sur l'application de la premi\`ere moyenne
arithm\'etique dans la th\'eorie des
s\'eries de fonctions orthogonales [On
the application of the first arithmetic
mean to the theory of series of orthogonal
functions]},
JOURNAL = {Fundam. Math.},
FJOURNAL = {Fundamenta Mathematicae},
VOLUME = {10},
YEAR = {1927},
PAGES = {356--362},
URL = {http://matwbn.icm.edu.pl/ksiazki/fm/fm10/fm10120.pdf},
NOTE = {JFM:53.0267.04.},
ISSN = {0016-2736},
}
J. Marcinkiewicz and A. Zygmund :
“A theorem of Lusin ,”
Duke Math. J.
4 : 3
(1938 ),
pp. 473–485 .
MR
1546069
JFM
64.0268.01
Zbl
0019.42001
article
People
BibTeX
@article {key1546069m,
AUTHOR = {Marcinkiewicz, J. and Zygmund, A.},
TITLE = {A theorem of {L}usin},
JOURNAL = {Duke Math. J.},
FJOURNAL = {Duke Mathematical Journal},
VOLUME = {4},
NUMBER = {3},
YEAR = {1938},
PAGES = {473--485},
DOI = {10.1215/S0012-7094-38-00440-5},
NOTE = {MR:1546069. Zbl:0019.42001. JFM:64.0268.01.},
ISSN = {0012-7094},
CODEN = {DUMJAO},
}
A. Zygmund :
“On the convergence and summability of power series on the circle of convergence, I ,”
Fundam. Math.
30
(1938 ),
pp. 170–196 .
Part II was published in Proc. London Math. Soc. 47 :1 .
JFM
64.1054.01
Zbl
0019.01602
article
BibTeX
@article {key0019.01602z,
AUTHOR = {Zygmund, Antoni},
TITLE = {On the convergence and summability of
power series on the circle of convergence,
{I}},
JOURNAL = {Fundam. Math.},
FJOURNAL = {Fundamenta Mathematicae},
VOLUME = {30},
YEAR = {1938},
PAGES = {170--196},
URL = {http://matwbn.icm.edu.pl/ksiazki/fm/fm30/fm30124.pdf},
NOTE = {Part II was published in \textit{Proc.
London Math. Soc.} \textbf{47}:1. Zbl:0019.01602.
JFM:64.1054.01.},
ISSN = {0016-2736},
}
A. Zygmund :
“On certain integrals ,”
Trans. Am. Math. Soc.
55
(1944 ),
pp. 170–204 .
MR
0009966
Zbl
0061.13902
article
Abstract
BibTeX
The present paper consists of three parts. The first two treat certain problems left open on the one hand by Littlewood and Paley, on the other by Marcinkiewicz. It turns out that these problems have close connection with each other. The remaining part is entirely independent of the first two and deals with absolute summability \( A \) of series. Its inclusion here may be explained by the fact that the integral it leads to is a limiting case of a certain family of integrals, another member of which plays an important role in §1.
@article {key0009966m,
AUTHOR = {Zygmund, A.},
TITLE = {On certain integrals},
JOURNAL = {Trans. Am. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {55},
YEAR = {1944},
PAGES = {170--204},
DOI = {10.1090/S0002-9947-1944-0009966-5},
NOTE = {MR:0009966. Zbl:0061.13902.},
ISSN = {0002-9947},
}
A. Zygmund :
“Proof of a theorem of Littlewood and Paley ,”
Bull. Am. Math. Soc.
51 : 6
(1945 ),
pp. 439–446 .
MR
0012306
Zbl
0060.14703
article
BibTeX
@article {key0012306m,
AUTHOR = {Zygmund, A.},
TITLE = {Proof of a theorem of {L}ittlewood and
{P}aley},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {51},
NUMBER = {6},
YEAR = {1945},
PAGES = {439--446},
DOI = {10.1090/S0002-9904-1945-08374-8},
NOTE = {MR:0012306. Zbl:0060.14703.},
ISSN = {0002-9904},
}
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},
}
A. Zygmund :
“On the Littlewood–Paley function \( g^*(\theta) \) ,”
Proc. Natl. Acad. Sci. U. S. A.
42 : 4
(April 1956 ),
pp. 208–212 .
MR
0077700
Zbl
0072.07201
article
BibTeX
@article {key0077700m,
AUTHOR = {Zygmund, A.},
TITLE = {On the {L}ittlewood--{P}aley function
\$g^*(\theta)\$},
JOURNAL = {Proc. Natl. Acad. Sci. U. S. A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {42},
NUMBER = {4},
MONTH = {April},
YEAR = {1956},
PAGES = {208--212},
DOI = {10.1073/pnas.42.4.208},
NOTE = {MR:0077700. Zbl:0072.07201.},
ISSN = {0027-8424},
}
M. Weiss and A. Zygmund :
“A note on smooth functions ,”
Nederl. Akad. Wetensch. Proc. Ser. A
62 : 1
(1959 ),
pp. 52–58 .
MR
0107122
Zbl
0085.05701
article
People
BibTeX
@article {key0107122m,
AUTHOR = {Weiss, Mary and Zygmund, Antoni},
TITLE = {A note on smooth functions},
JOURNAL = {Nederl. Akad. Wetensch. Proc. Ser. A},
FJOURNAL = {Nederlandse Akademie van Wetenschappen.
Proceedings. Series A. Indagationes
Mathematicae},
VOLUME = {62},
NUMBER = {1},
YEAR = {1959},
PAGES = {52--58},
DOI = {10.1007/978-94-009-1045-4_16},
NOTE = {MR:0107122. Zbl:0085.05701.},
ISSN = {0023-3358},
}
A. Zygmund :
Trigonometric series ,
2nd edition,
vol. I .
Cambridge University Press (New York ),
1959 .
First volume of an enlarged edition of 1935 original .
MR
0107776
Zbl
0085.05601
book
BibTeX
@book {key0107776m,
AUTHOR = {Zygmund, A.},
TITLE = {Trigonometric series},
EDITION = {2nd},
VOLUME = {I},
PUBLISHER = {Cambridge University Press},
ADDRESS = {New York},
YEAR = {1959},
PAGES = {xii+383},
NOTE = {First volume of an enlarged edition
of 1935 original. MR:0107776. Zbl:0085.05601.},
}
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},
}
E. M. Stein and A. Zygmund :
“On the differentiability of functions ,”
Studia Math.
23 : 3
(1963–1964 ),
pp. 247–283 .
Dedicated to E. Hille on the occasion of his 70th birthday.
MR
0158955
Zbl
0122.30203
article
Abstract
People
BibTeX
@article {key0158955m,
AUTHOR = {Stein, E. M. and Zygmund, A.},
TITLE = {On the differentiability of functions},
JOURNAL = {Studia Math.},
FJOURNAL = {Studia Mathematica. Polska Akademia
Nauk},
VOLUME = {23},
NUMBER = {3},
YEAR = {1963--1964},
PAGES = {247--283},
URL = {http://matwbn.icm.edu.pl/ksiazki/sm/sm23/sm23116.pdf},
NOTE = {Dedicated to E. Hille on the occasion
of his 70th birthday. MR:0158955. Zbl:0122.30203.},
ISSN = {0039-3223},
}