### Complete Bibliography

[1] : “On a class of stochastic approximation processes,” Ann. Math. Stat. 27 : 4 (1956), pp. 1044–1059. This appears to be an abridged version of the author’s 1956 PhD thesis. MR 85653 Zbl 0075.13803 article

[2]
:
On a certain class of stochastic approximation processes.
Ph.D. thesis,
The University of North Carolina at Chapel Hill,
1956.
Advised by W. Höffding.
An abridged version of this was published in *Ann. Math. Stat.* **27**:4 (1956).
MR
2938781
phdthesis

[3] : “On the existence of a best approximation of one distribution function by another of a given type,” Ann. Math. Stat. 30 : 3 (1959), pp. 738–742. MR 106522 Zbl 0096.13102 article

[4] : “Effect on the minimal complete class of tests of changes in the testing problem,” Ann. Math. Stat. 31 : 2 (1960), pp. 325–331. MR 117846 Zbl 0119.15305 article

[5] : “Sufficiency in the undominated case,” Ann. Math. Stat. 32 : 4 (1961), pp. 1191–1200. MR 131287 Zbl 0221.62003 article

[6] : “Iterates of conditional expectation operators,” Proc. Am. Math. Soc. 12 : 3 (1961), pp. 490–495. MR 142144 Zbl 0106.33201 article

[7] : “On the order structure of the set of sufficient subfields,” Ann. Math. Stat. 33 : 2 (1962), pp. 596–599. MR 137227 Zbl 0127.34808 article

[8] : “Semi-Gaussian subspaces,” Trans. Am. Math. Soc. 104 : 1 (1962), pp. 123–131. MR 138986 Zbl 0131.35001 article

[9] : “Successive conditional expectations of an integrable function,” Ann. Math. Stat. 33 : 3 (1962), pp. 887–893. MR 143246 Zbl 0128.12602 article

[10] : “Optimum properties and admissibility of sequential tests,” Ann. Math. Stat. 34 : 1 (1963), pp. 1–17. MR 148160 Zbl 0113.13005 article

[11] : “Maximal inequalities as necessary conditions for almost everywhere convergence,” Z. Wahrscheinlichkeitstheor. Verw. Geb. 3 : 1 (March 1964), pp. 75–88. MR 189110 Zbl 0134.14602 article

[12] : “Martingale transforms,” Ann. Math. Statist. 37 (1966), pp. 1494–1504. MR 0208647 Zbl 0306.60030 article

[13] : “Independent sequences with the Stein property,” Ann. Math. Stat. 39 : 4 (1968), pp. 1282–1288. MR 228045 Zbl 0162.49404 article

[14] : “Extrapolation and interpolation of quasi-linear operators on martingales,” Acta Math. 124 (1970), pp. 249–304. MR 0440695 Zbl 0223.60021 article

[15]
:
“A maximal function characterization of the class __\( H^{p} \)__,”
Trans. Amer. Math. Soc.
157
(1971),
pp. 137–153.
MR
0274767
Zbl
0223.30048
article

[16] : “Martingale inequalities,” pp. 1–8 in Martingales (Oberwolfach, Germany, 17–23 May 1970). Lecture Notes in Mathematics 190. Springer (Berlin), 1971. MR 372985 incollection

[17] : “Inequalities for operators on martingales,” pp. 551–557 in Actes du Congrès International des Mathématiciens (Nice, France, 1–10 September 1970), vol. 2. Gauthier-Villars (Paris), 1971. MR 420830 Zbl 0245.60041 incollection

[18]
:
“Extrapolation and interpolation of quasi-linear operators on martingales,”
Matematika
15 : 3
(1971),
pp. 91–141.
Russian translation of article published in *Acta Math.* **124** (1970).
Zbl
0223.60022
article

[19] : “Distribution function inequalities for the area integral,” pp. 527–544 in Collection of articles honoring the completion by Antoni Zygmund of 50 years of scientific activity, VI, published as Studia Math. 44 : 6. Państwowe Wydawnictwo Naukowe (Warsaw), 1972. MR 340557 Zbl 0219.31009 incollection

[20] : “Integral inequalities for convex functions of operators on martingales,” pp. 223–240 in Proceedings of the sixth Berkeley symposium on mathematical statistics and probability (Berkeley, CA, 21 June–18 July 1970), vol. 2: Probability theory. Edited by L. Le Cam, J. Neyman, and E. L. Scott. University of California Press (Berkeley and Los Angeles, CA), 1972. MR 400380 Zbl 0253.60056 incollection

[21] : “Boundary behaviour of harmonic functions in a half-space and Brownian motion,” Ann. Inst. Fourier (Grenoble) 23 : 4 (1973), pp. 195–212. MR 365691 Zbl 0253.31010 article

[22] : “Distribution function inequalities for martingales,” Ann. Probab. 1 : 1 (1973), pp. 19–42. MR 365692 Zbl 0301.60035 article

[23]
:
“__\( H^p \)__ spaces and exit times of Brownian motion,”
Bull. Am. Math. Soc.
81 : 3
(May 1975),
pp. 556–558.
MR
362519
Zbl
0321.60059
article

[24]
:
“One-sided maximal functions and __\( H^p \)__,”
J. Funct. Anal.
18 : 4
(April 1975),
pp. 429–454.
MR
365693
Zbl
0294.31005
article

[25] : “Harmonic analysis and probability,” pp. 136–149 in Studies in harmonic analysis (Chicago, 1974). Edited by J. M. Ash. MAA Studies in Mathematics 13. Mathematical Association of America (Washington, DC), 1976. MR 463788 Zbl 0339.42011 incollection

[26] : “Brownian motion and classical analysis,” pp. 5–14 in Probability (Urbana, IL, March 1976). Edited by J. L. Doob. Proceedings of Symposia in Pure Mathematics 31. American Mathematical Society (Providence, RI), 1977. MR 474524 Zbl 0365.60075 incollection

[27] : “Exit times of Brownian motion, harmonic majorization, and Hardy spaces,” Adv. Math. 26 : 2 (November 1977), pp. 182–205. MR 474525 Zbl 0372.60112 article

[28]
:
“Approximation of __\( L^1 \)__-bounded martingales by martingales of bounded variation,”
Proc. Am. Math. Soc.
72 : 1
(October 1978),
pp. 166–169.
MR
494472
Zbl
0387.60048
article

[29] : “Boundary value estimation of the range of an analytic function,” Mich. Math. J. 25 : 2 (1978), pp. 197–211. MR 501568 Zbl 0372.30026 article

[30] : “A sharp inequality for martingale transforms,” Ann. Probab. 7 : 5 (1979), pp. 858–863. MR 542135 Zbl 0416.60047 article

[31] : “Martingale theory and harmonic analysis in Euclidean spaces,” pp. 283–301 in Harmonic analysis in Euclidean spaces (Williamstown, MA, 10–28 July 1978), Part 2. Edited by G. Weiss and S. Wainger. Proceedings of Symposia in Pure Mathematics 35. American Mathematical Society (Providence, RI), 1979. MR 545315 Zbl 0417.60055 incollection

[32] : “Weak inequalities for exit times and analytic functions,” pp. 27–34 in Probability theory (Warsaw, 6 February–11 June 1976). Edited by Z. Ciesielski. Banach Center Publications 5. PWN (Warsaw), 1979. MR 561465 Zbl 0416.60048 incollection

[33]
:
“Brownian motion and the Hardy spaces __\( H^p \)__,”
pp. 97–118
in
Aspects of contemporary complex analysis
(Durham, UK, 1–20 July 1979).
Edited by D. A. Brannan and J. Clunie.
Academic Press (London and New York),
1980.
MR
623466
Zbl
0497.30028
incollection

[34] : “Some new inequalities in complex analysis (and what they do),” Real Anal. Exch. 5 : 1 (1980), pp. 124–127. Zbl 0423.30023 article

[35] : “A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional,” Ann. Probab. 9 : 6 (1981), pp. 997–1011. MR 632972 Zbl 0474.60036 article

[36] : “Martingale transforms and the geometry of Banach spaces,” pp. 35–50 in Probability in Banach spaces, III (Medford, MA, 4–16 August 1980). Edited by A. Beck. Lecture Notes in Mathematics 860. Springer (Berlin), 1981. MR 647954 Zbl 0471.60012 incollection

[37]
:
“A nonlinear partial differential equation and the unconditional constant of the Haar system in __\( L^p \)__,”
Bull. Am. Math. Soc. (N.S.)
7 : 3
(1982),
pp. 591–595.
Research announcement.
MR
670133
Zbl
0504.46022
article

[38] : “A geometric condition that implies the existence of certain singular integrals of Banach-space-valued functions,” pp. 270–286 in Conference on harmonic analysis in honor of Antoni Zygmund (Chicago, 23–28 March 1981), vol. 1. Edited by W. Beckner, A. P. Calderón, R. Fefferman, and P. W. Jones. Wadsworth Mathematics Series. Wadsworth (Belmont, CA), 1983. MR 730072 incollection

[39] : “Boundary value problems and sharp inequalities for martingale transforms,” Ann. Probab. 12 : 3 (1984), pp. 647–702. MR 744226 Zbl 0556.60021 article

[40] : “An elementary proof of an inequality of R. E. A. C. Paley,” Bull. London Math. Soc. 17 : 5 (September 1985), pp. 474–478. MR 806015 Zbl 0566.46014 article

[41] : “An extension of a classical martingale inequality,” pp. 21–30 in Probability theory and harmonic analysis (New York). Edited by J.-A. Chao and W. Woyczyński. Pure and Applied Mathematics 98. Dekker, 1986. MR 830228 Zbl 0594.60020 incollection

[42] : “Martingales and Fourier analysis in Banach spaces,” pp. 61–108 in Probability and analysis (Varenna, Italy, 31 May–8 June 1985). Edited by G. Letta and M. Pratelli. Lecture Notes in Mathematics 1206. Springer (Berlin), 1986. MR 864712 Zbl 0605.60049 incollection

[43]
:
“A sharp and strict __\( L^p \)__-inequality for stochastic integrals,”
Ann. Probab.
15 : 1
(1987),
pp. 268–273.
MR
877602
Zbl
0617.60042
article

[44] : “A proof of Pełczyński’s conjecture for the Haar system,” Studia Math. 91 : 1 (1988), pp. 79–83. MR 957287 Zbl 0652.42012 article

[45] : “Sharp inequalities for martingales and stochastic integrals,” pp. 75–94 in Colloque Paul Lévy sur les processus stochastiques [Paul Lévy colloquium on stochastic processes] (Palaiseau, France, 22–26 June 1987). Edited by L. Schwartz. Astérisque 157–158. Sociét’e Mathématique de France (Paris), 1988. MR 976214 Zbl 0656.60055 incollection

[46] : “Differential subordination of harmonic functions and martingales,” pp. 1–23 in Harmonic analysis and partial differential equations (El Escorial, Spain, 9–13 June 1987). Edited by J. García-Cuerva. Lecture Notes in Mathematics 1384. Springer (Berlin), 1989. MR 1013814 Zbl 0675.31003 incollection

[47] : “On the number of escapes of a martingale and its geometrical significance,” pp. 159–178 in Almost everywhere convergence: Proceedings of the international conference on almost everywhere convergence in probability and ergodic theory (Columbus, OH, 11–14 June 1988). Edited by G. A. Edgar and L. Sucheston. Academic Press (Boston, MA), 1989. MR 1035244 Zbl 0685.60049 incollection

[48] : École d’été de probabilités de Saint-Flour XIX–1989 [12th Saint-Flour probability summer school–1989] (Saint-Flour, France, 16 August–2 September 1989). Edited by P. L. Hennequin. Lecture Notes in Mathematics 1464. Springer (Berlin), 1991. MR 1108182 Zbl 0722.00029 book

[49] : “Explorations in martingale theory and its applications,” pp. 1–66 in : École d’été de probabilités de Saint-Flour XIX–1989 [12th Saint-Flour probability summer school–1989] (Saint-Flour, France, 16 August–2 September 1989). Edited by P. L. Hennequin. Lecture Notes in Mathematics 1464. Springer (Berlin), 1991. MR 1108183 Zbl 0771.60033 incollection

[50] : “Book review: G. Pisier, ‘The volume of convex bodies and Banach space geometry’,” Bull. Am. Math. Soc. (N.S.) 25 : 1 (1991), pp. 140–145. MR 1567936 article

[51] “59 are chosen for National Academy of Sciences,” NYT (10 May 1992), pp. 1001024. article

[52] : “Strong differential subordination and stochastic integration,” Ann. Probab. 22 : 2 (1994), pp. 995–1025. MR 1288140 Zbl 0816.60046 article

[53] : “Sharp norm comparison of martingale maximal functions and stochastic integrals,” pp. 343–358 in Proceedings of the Norbert Wiener Centenary Congress, 1994 (East Lansing, MI, 27 November–3 December 1994). Edited by V. Mandrekar and P. R. Masani. Proceedings of Symposia in Applied Mathematics 52. American Mathematical Society (Providence, RI), 1997. MR 1440921 Zbl 0899.60040 incollection

[54] : “Some extremal problems in martingale theory and harmonic analysis,” pp. 99–115 in Harmonic analysis and partial differential equations: Essays in honor of Alberto P. Calderón (Chicago, 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 Calderón’s 75th birthday. MR 1743857 Zbl 0954.60034 incollection

[55] : “Martingales and singular integrals in Banach spaces,” Chapter 6, pp. 233–269 in Handbook of the geometry of Banach spaces, vol. 1. Edited by W. B. Johnson and J. Lindenstrauss. Elsevier (Amsterdam), 2001. MR 1863694 Zbl 1029.46007 incollection

[56] : “The best constant in the Davis inequality for the expectation of the martingale square function,” Trans. Am. Math. Soc. 354 : 1 (2002), pp. 91–105. MR 1859027 Zbl 0984.60041 article

[57] : “Joseph Leo Doob, 1910–2004,” Stochastic Process. Appl. 115 : 7 (July 2005), pp. 1061–1072. MR 2147241 Zbl 1073.01516 article

[58] : “Foreword,” pp. v in Joseph Doob: A collection of mathematical articles in his memory, published as Ill. J. Math. 50 : 1–4. Duke University Press (Durham, NC), 2006. MR 2247820 incollection

[59] : “Joseph Leo Doob (1910–2004),” pp. vii–viii in Joseph Doob: A collection of mathematical articles in his memory, published as Ill. J. Math. 50 : 1–4. Issue edited by D. Burkholder. Duke University Press (Durham, NC), 2006. MR 2247821 Zbl 1130.01303 incollection

[60] Joseph Doob: A collection of mathematical articles in his memory, published as Ill. J. Math. 50 : 1–4. Issue edited by D. Burkholder. Duke University Press (Durham, NC), 2007. Zbl 1120.60002 book

[61] : “Comments on (5), (14), (22), (30), and (31),” pp. 553–558 in Selected papers of Alberto P. Calderón with commentary. Edited by A. Bellow, C. E. Kenig, and P. Malliavin. AMS Collected Works 21. American Mathematial Society (Providence, RI), 2008. MR 2435333 incollection

[62] A collection of articles in honor of Don Burkholder, published as Ill. J. Math. 54 : 4. Issue edited by R. Bauer, R. Song, and R. Sowers. University of Illinois, Department of Mathematics (Urbana, IL), 2010. Zbl 1328.01047 book

[63] : Illinois mathematician elected fellow of AAAS, 11 January 2011. Illinois News Bureau online article. misc

[64] : Selected works of Donald L. Burkholder. Edited by B. Davis and R. Song. Selected Works in Probability and Statistics. Springer (Berlin), 2011. MR 2850314 Zbl 1271.01046 book

[65] “Obituary: Donald Burkholder,” The News-Gazette (17 April 2013). article

[66] Memorial issue for Donald Burkholder (1927–2013), published as Ann. Probab. 45 : 1. Issue edited by R. Bañuelos and B. Davis. Institute of Mathematical Statistics (Beachwood, OH), 2017. book

[67] : “Introduction to memorial issue for Donald Burkholder (1927–2013),” pp. 1–3 in Memorial issue for Donald Burkholder (1927–2013), published as Ann. Probab. 45 : 1. Issue edited by R. Bañuelos and B. Davis. Institute of Mathematical Statistics (Beachwood, OH), 2017. MR 3601643 Zbl 1359.01025 incollection