Selected Publications of
Donald L. Burkholder

 5. Sufficiency in the undominated case, Ann. Math. Statist. 32 (1961), 1191-1200.
 6. Semi-Gaussian subspaces, Trans. Amer. Math. Soc. 104 (1962), 123-131.
 7. On the order structure of the set of sufficient subfields, Ann. Math. Statist. 33 (1962), 596-599.
 8. Successive conditional expectations of an integrable function, Ann. Math. Statist. 33 (1962), 887-893.
10. Maximal inequalities as necessary conditions for almost everywhere convergence, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 (1964), 75-88.
11. Martingale transforms, Ann. Math. Statist. 37 (1966), 1494-1504.
14. Extrapolation and interpolation of quasi-linear operators on martingales, with R. F. Gundy, Acta Math. 124 (1970), 249-304 .
16. A maximal function characterization of the class H^p, with R. F. Gundy and M. L. Silverstein, Trans. Amer. Math. Soc. 157 (1971), 137-153 .
17. Inequalities for operators on martingales, Proc. International Congress of Mathematicians (Nice, France, 1970) 2 (1971), 551-557.
18. Integral inequalities for convex functions of operators on martingales, with B. J. Davis and R. F. Gundy, Proc. Sixth Berkeley Symp. Math. Statist. and Prob. 2 (1972), 223-240.
19. Distribution function inequalities for the area integral, with R. F. Gundy, Studia Math. 44 (1972), 527-544.
20. Distribution function inequalities for martingales, Ann. Probab. 1 (1973), 19-42.
23. One-sided maximal functions and H^p, J. Funct. Anal. 18 (1975), 429-454.
26. Exit times of Brownian motion, harmonic majorization, and Hardy spaces, Advances in Math. 26 (1977), 182-205.
29. Boundary value estimation of the range of an analytic function, Michigan Math. J. 25 (1978), 197-211.
32. Martingale theory and harmonic analysis in Euclidean spaces, Proc. of Symposia in Pure Math. 35: 2 (1979), 283-301.
34. Brownian motion and the Hardy spaces H^p, in "Aspects of Contemporary Complex Analysis," edited by D. A. Brannan and J. G. Clunie, Academic Press, London, 1980, pp.97-118.
35. A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional, Ann. Probab. 9 (1981), 997-1011.
37. A nonlinear partial differential equation and the unconditional constant of the Haar system in L^p, Bull. Amer. Math. Soc. 7 (1982), 591-595.
38. A geometric condition that implies the existence of certain singular integrals of Banach-space-valued functions, in "Conference on Harmonic Analysis in Honor of Antoni Zygmund," (Chicago, 1981), edited by William Beckner, Alberto P. Calder'on, Robert Fefferman, and Peter W. Jones. Wadsworth, Belmont, California, 1983, pp. 270-286.
39. Boundary value problems and sharp inequalities for martingale transforms, Ann. Probab. 12 (1984), 647-702.
40. An elementary proof of an inequality of R. E. A. C. Paley, Bull. London Math. Soc. 17 (1985), 474-478.
42. Martingales and Fourier analysis in Banach spaces, C.I.M.E. Lectures (Varenna (Como), Italy, 1985), Lecture Notes in Mathematics 1206 (1986), 61-108.
43. A sharp and strict L^p-inequality for stochastic integrals, Ann. Probab. 15 (1987 ), 268-273.
44. A proof of Pelczy'nski's conjecture for the Haar system, Studia Math. 91(1988), 79-83.
45. Sharp inequalities for martingales and stochastic integrals, Colloque Paul L'evy (Palaiseau,1987), Ast'erisque 157-158 (1988), 75-94.
46. Differential subordination of harmonic functions and martingales, Harmonic Analysis and Partial Differential Equations (El Escorial, 1987), Lecture Notes in Mathematics 1384 (1989), 1-23.
47. On the number of escapes of a martingale and its geometrical significance, in "Almost Everywhere Convergence," edited by Gerald A. Edgar and Louis Sucheston. Academic Press, New York, 1989, pp. 159-178.
48. Explorations in martingale theory and its applications, 'Ecole d'Et'e de Probabilit'es de Saint-Flour XIX-1989, Lecture Notes in Mathematics 1464 (1991), 1-66.
50. Strong differential subordination and stochastic integration, Ann. Probab. 22 (1994), 995-1025.
51. Sharp norm comparison of martingale maximal functions and stochastic integrals, Proceedings of the Norbert Wiener Centenary Congress (East Lansing, MI, 1994), 343--358, Proc. Sympos. Appl. Math. 52, Amer. Math. Soc., Providence, RI (1997).
52. Some extremal problems in martingale theory and harmonic analysis, Harmonic Analysis and Partial Differential Equations (Chicago, 1996), 99--115, Chicago Lectures in Math. Univ. Chicago Press, Chicago, 1999.
53. Martingales and singular integtrals in Banach spaces, Handbook on the Geometry of Banach spaces, Volume 1, edited by William B. Johnson and Joram Lindenstrauss, Elsevier, 2001, pp. 233-269.
54. The best constant in the Davis inequality for the expectation of the martingale square function, Trans. Amer. Math. Soc. 354 (2002), Number 1 (January issue), pp. 91--105.
58. Comments on [5], [14], [22], [30], and [31]. These are part of the Calderon Selecta volume, to appear. download pdf

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