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Burkholder, Donald L. (b. 1927 d. 2013)

Author ID: burkholder.donald-l Recent zbMATH articles by "Burkholder, Donald L."
Published as: Burkholder, D. L.; Burkholder, Donald L.; Burkholder, Donald; Burkholder, D.
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Publications by Year

Citations contained in zbMATH Open

47 Publications have been cited 1,965 times in 1,320 Documents Cited by Year
Distribution function inequalities for martingales. Zbl 0301.60035
Burkholder, D. L.
344
1973
Martingale transforms. Zbl 0306.60030
Burkholder, D. L.
195
1966
Boundary value problems and sharp inequalities for martingale transforms. Zbl 0556.60021
Burkholder, D. L.
176
1984
Extrapolation and interpolation of quasi-linear operators on martingales. Zbl 0223.60021
Burkholder, D. L.; Gundy, R. F.
163
1970
A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional. Zbl 0474.60036
Burkholder, D. L.
105
1981
Explorations in martingale theory and its applications. Zbl 0771.60033
Burkholder, Donald L.
104
1991
Integral inequalities for convex functions of operators on martingales. Zbl 0253.60056
Burkholder, D. L.; Davis, B. J.; Gundy, R. F.
98
1972
Martingales and singular integrals in Banach spaces. Zbl 1029.46007
Burkholder, Donald L.
91
2001
A maximal function characterization of the class \(H^{\mathfrak p}\). Zbl 0223.30048
Burkholder, D. L.; Gundy, R. F.; Silverstein, M. L.
74
1971
Sharp inequalities for martingales and stochastic integrals. Zbl 0656.60055
Burkholder, Donald L.
69
1988
Martingales and Fourier analysis in Banach spaces. Zbl 0605.60049
Burkholder, Donald L.
68
1986
Exit times of Brownian motion, harmonic majorization, and Hardy spaces. Zbl 0372.60112
Burkholder, D. L.
65
1977
Distribution function inequalities for the area integral. Zbl 0219.31009
Burkholder, D. L.; Gundy, R. F.
39
1972
Successive conditional expectations of an integrable function. Zbl 0128.12602
Burkholder, D. L.
38
1962
Iterates of conditional expectation operators. Zbl 0106.33201
Burkholder, D. L.; Chow, Y. S.
28
1961
The best constant in the Davis inequality for the expectation of the martingale square function. Zbl 0984.60041
Burkholder, Donald L.
25
2002
A proof of Pełczyński’s conjecture for the Haar system. Zbl 0652.42012
Burkholder, Donald L.
24
1988
Strong differential subordination and stochastic integration. Zbl 0816.60046
Burkholder, Donald L.
22
1994
Maximal inequalities as necessary conditions for almost everywhere convergence. Zbl 0134.14602
Burkholder, D. L.
19
1964
Sufficiency in the undominated case. Zbl 0221.62003
Burkholder, D. L.
19
1961
A sharp and strict \(L^ p\)-inequality for stochastic integrals. Zbl 0617.60042
Burkholder, D. L.
18
1987
Differential subordination of harmonic functions and martingales. Zbl 0675.31003
Burkholder, Donald L.
18
1989
Sharp norm comparison of martingale maximal functions and stochastic integrals. Zbl 0899.60040
Burkholder, Donald L.
17
1997
Independent sequences with the Stein property. Zbl 0162.49404
Burkholder, D. L.
16
1968
On a class of stochastic approximation processes. Zbl 0075.13803
Burkholder, D. L.
16
1956
One-sided maximal functions and H\(^p\). Zbl 0294.31005
Burkholder, D. L.
12
1975
An elementary proof of an inequality of R. E. A. C. Paley. Zbl 0566.46014
Burkholder, D. L.
12
1985
Martingale transforms and the geometry of Banach spaces. Zbl 0471.60012
Burkholder, D. L.
12
1981
Optimum properties and admissibility of sequential tests. Zbl 0113.13005
Burkholder, D. L.; Wijsman, R. A.
11
1963
A sharp inequality for martingale transforms. Zbl 0416.60047
Burkholder, D. L.
11
1979
A nonlinear partial differential equation and the unconditional constant of the Haar system in \(L^ p\). Zbl 0504.46022
Burkholder, D. L.
9
1982
An extension of a classical martingale inequality. Zbl 0594.60020
Burkholder, Donald L.
9
1986
Semi-Gaussian subspaces. Zbl 0131.35001
Burkholder, D. L.
8
1962
Boundary behavior of harmonic functions in a half-space and Brownian motion. Zbl 0253.31010
Burkholder, D. L.; Gundy, Richard F.
5
1973
Martingale theory and harmonic analysis in Euclidean spaces. Zbl 0417.60055
Burkholder, D. L.
4
1979
Boundary value estimation of the range of an analytic function. Zbl 0372.30026
Burkholder, D. L.
3
1978
On the number of escapes of a martingale and its geometrical significance. Zbl 0685.60049
Burkholder, Donald L.
3
1989
Some extremal problems in martingale theory and harmonic analysis. Zbl 0954.60034
Burkholder, Donald L.
2
1999
Joseph Leo Doob, 1910–2004. Zbl 1073.01516
Burkholder, Donald; Protter, Philip
2
2005
Extrapolation and interpolation of quasi-linear operators on martingales. Zbl 0223.60022
Burkholder, D. L.; Gundy, R. F.
2
1971
On the order structure of the set of sufficient subfields. Zbl 0127.34808
Burkholder, D.
2
1962
Selected works of Donald L. Burkholder. Edited by Burgess Davis and Renming Song. Zbl 1271.01046
Burkholder, Donald L.
2
2011
Brownian motion and the Hardy spaces \(H^ p\). Zbl 0497.30028
Burkholder, D. L.
1
1980
\(H^p\) spaces and exit times of Brownian motion. Zbl 0321.60059
Burkholder, D. L.
1
1975
Harmonic analysis and probability. Zbl 0339.42011
Burkholder, D. L.
1
1976
Approximation of \(L^1\)-bounded martingales by martingales of bounded variation. Zbl 0387.60048
Burkholder, D. L.; Shintani, T.
1
1978
Weak inequalities for exit times and analytic functions. Zbl 0416.60048
Burkholder, D. L.
1
1979
Selected works of Donald L. Burkholder. Edited by Burgess Davis and Renming Song. Zbl 1271.01046
Burkholder, Donald L.
2
2011
Joseph Leo Doob, 1910–2004. Zbl 1073.01516
Burkholder, Donald; Protter, Philip
2
2005
The best constant in the Davis inequality for the expectation of the martingale square function. Zbl 0984.60041
Burkholder, Donald L.
25
2002
Martingales and singular integrals in Banach spaces. Zbl 1029.46007
Burkholder, Donald L.
91
2001
Some extremal problems in martingale theory and harmonic analysis. Zbl 0954.60034
Burkholder, Donald L.
2
1999
Sharp norm comparison of martingale maximal functions and stochastic integrals. Zbl 0899.60040
Burkholder, Donald L.
17
1997
Strong differential subordination and stochastic integration. Zbl 0816.60046
Burkholder, Donald L.
22
1994
Explorations in martingale theory and its applications. Zbl 0771.60033
Burkholder, Donald L.
104
1991
Differential subordination of harmonic functions and martingales. Zbl 0675.31003
Burkholder, Donald L.
18
1989
On the number of escapes of a martingale and its geometrical significance. Zbl 0685.60049
Burkholder, Donald L.
3
1989
Sharp inequalities for martingales and stochastic integrals. Zbl 0656.60055
Burkholder, Donald L.
69
1988
A proof of Pełczyński’s conjecture for the Haar system. Zbl 0652.42012
Burkholder, Donald L.
24
1988
A sharp and strict \(L^ p\)-inequality for stochastic integrals. Zbl 0617.60042
Burkholder, D. L.
18
1987
Martingales and Fourier analysis in Banach spaces. Zbl 0605.60049
Burkholder, Donald L.
68
1986
An extension of a classical martingale inequality. Zbl 0594.60020
Burkholder, Donald L.
9
1986
An elementary proof of an inequality of R. E. A. C. Paley. Zbl 0566.46014
Burkholder, D. L.
12
1985
Boundary value problems and sharp inequalities for martingale transforms. Zbl 0556.60021
Burkholder, D. L.
176
1984
A nonlinear partial differential equation and the unconditional constant of the Haar system in \(L^ p\). Zbl 0504.46022
Burkholder, D. L.
9
1982
A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional. Zbl 0474.60036
Burkholder, D. L.
105
1981
Martingale transforms and the geometry of Banach spaces. Zbl 0471.60012
Burkholder, D. L.
12
1981
Brownian motion and the Hardy spaces \(H^ p\). Zbl 0497.30028
Burkholder, D. L.
1
1980
A sharp inequality for martingale transforms. Zbl 0416.60047
Burkholder, D. L.
11
1979
Martingale theory and harmonic analysis in Euclidean spaces. Zbl 0417.60055
Burkholder, D. L.
4
1979
Weak inequalities for exit times and analytic functions. Zbl 0416.60048
Burkholder, D. L.
1
1979
Boundary value estimation of the range of an analytic function. Zbl 0372.30026
Burkholder, D. L.
3
1978
Approximation of \(L^1\)-bounded martingales by martingales of bounded variation. Zbl 0387.60048
Burkholder, D. L.; Shintani, T.
1
1978
Exit times of Brownian motion, harmonic majorization, and Hardy spaces. Zbl 0372.60112
Burkholder, D. L.
65
1977
Harmonic analysis and probability. Zbl 0339.42011
Burkholder, D. L.
1
1976
One-sided maximal functions and H\(^p\). Zbl 0294.31005
Burkholder, D. L.
12
1975
\(H^p\) spaces and exit times of Brownian motion. Zbl 0321.60059
Burkholder, D. L.
1
1975
Distribution function inequalities for martingales. Zbl 0301.60035
Burkholder, D. L.
344
1973
Boundary behavior of harmonic functions in a half-space and Brownian motion. Zbl 0253.31010
Burkholder, D. L.; Gundy, Richard F.
5
1973
Integral inequalities for convex functions of operators on martingales. Zbl 0253.60056
Burkholder, D. L.; Davis, B. J.; Gundy, R. F.
98
1972
Distribution function inequalities for the area integral. Zbl 0219.31009
Burkholder, D. L.; Gundy, R. F.
39
1972
A maximal function characterization of the class \(H^{\mathfrak p}\). Zbl 0223.30048
Burkholder, D. L.; Gundy, R. F.; Silverstein, M. L.
74
1971
Extrapolation and interpolation of quasi-linear operators on martingales. Zbl 0223.60022
Burkholder, D. L.; Gundy, R. F.
2
1971
Extrapolation and interpolation of quasi-linear operators on martingales. Zbl 0223.60021
Burkholder, D. L.; Gundy, R. F.
163
1970
Independent sequences with the Stein property. Zbl 0162.49404
Burkholder, D. L.
16
1968
Martingale transforms. Zbl 0306.60030
Burkholder, D. L.
195
1966
Maximal inequalities as necessary conditions for almost everywhere convergence. Zbl 0134.14602
Burkholder, D. L.
19
1964
Optimum properties and admissibility of sequential tests. Zbl 0113.13005
Burkholder, D. L.; Wijsman, R. A.
11
1963
Successive conditional expectations of an integrable function. Zbl 0128.12602
Burkholder, D. L.
38
1962
Semi-Gaussian subspaces. Zbl 0131.35001
Burkholder, D. L.
8
1962
On the order structure of the set of sufficient subfields. Zbl 0127.34808
Burkholder, D.
2
1962
Iterates of conditional expectation operators. Zbl 0106.33201
Burkholder, D. L.; Chow, Y. S.
28
1961
Sufficiency in the undominated case. Zbl 0221.62003
Burkholder, D. L.
19
1961
On a class of stochastic approximation processes. Zbl 0075.13803
Burkholder, D. L.
16
1956
all top 5

Cited by 1,314 Authors

93 Osękowski, Adam
30 Bañuelos, Rodrigo
29 Jiao, Yong
20 Weisz, Ferenc
17 Volberg, Alexander Lvovich
16 Veraar, Mark C.
14 Nikolidakis, Eleftherios Nikolaos
13 Khoshnevisan, Davar
12 Wu, Lian
11 Betancor Perez, Jorge Juan
10 Bai, Zhi-Dong
10 Melas, Antonios D.
10 Mohan, Manil Thankamani
10 Sukochev, Fedor Anatol’evich
10 Xu, Quanhua
10 Yaroslavtsev, Ivan S.
10 Zhou, Dejian
9 Hall, Peter Gavin
9 Markowsky, Greg T.
9 Melbourne, Ian
8 Burkholder, Donald L.
8 Castro, Alejandro J.
8 Junge, Marius
8 Labbas, Rabah
8 Makasu, Cloud
8 Perkins, Edwin A.
8 Randrianantoanina, Narcisse
8 Yu, Lin
7 Boudabra, Maher
7 Gundy, Richard F.
7 Janakiraman, Prabhu
7 Liu, Peide
7 Maingot, Stéphane
7 Martell, José María (Chema)
7 Petermichl, Stefanie
7 Rodríguez-Mesa, Lourdes
7 Vasyunin, Vasiliĭ Ivanovich
7 Xie, Guangheng
7 Yang, Dachun
6 Astashkin, Sergeĭ Vladimir
6 Conus, Daniel
6 Davis, Burgess
6 Domelevo, Komla
6 Dziubański, Jacek
6 Fariña, Juan Carlos
6 Hitczenko, Paweł
6 Hytönen, Tuomas P.
6 Ivanisvili, Paata
6 Le Merdy, Christian
6 McConnell, Terry R.
6 Peligrad, Magda
6 Pérez, Carlos
6 Stolyarov, Dmitry M.
6 van Neerven, Jan M. A. M.
6 Wheeden, Richard Lee
6 Yor, Marc
6 Zanin, Dmitriy V.
6 Zatitskii, Pavel B.
5 de la Peña, Victor H.
5 Deblassie, Dante
5 DeBlassie, Richard Dante
5 Dragičević, Oliver
5 Fackler, Stephan
5 Gałązka, Tomasz
5 Gát, György
5 Geiss, Stefan
5 Hao, Zhiwei
5 Ho, Kwok-Pun
5 Joseph, Mathew
5 Kenig, Carlos Eduardo
5 Kikuchi, Masato
5 Kovač, Vjekoslav
5 Li, Deli
5 Li, Libo
5 Nazarov, Fedor L.
5 Parcet, Javier
5 Schechtman, Gideon
5 Seppäläinen, Timo
5 Shiu, Shang-Yuan
5 Sung, Soohak
5 Thorel, Alexandre
5 Weis, Lutz W.
5 Wu, Wei Biao
4 Akcoglu, Mustafa A.
4 Amenta, Alex
4 Arcozzi, Nicola
4 Bogdan, Krzysztof
4 Bourgain, Jean
4 Brzeźniak, Zdzisław
4 Brzozowski, Michał
4 Cox, Sonja Gisela
4 Cuny, Christophe
4 Deleaval, Luc
4 Fan, Chenjie
4 Gaposhkin, Vladimir Fedorovich
4 Giles, Michael B.
4 Gut, Allan
4 Lai, Tze Leung
4 Lin, Guihua
4 Medeghri, Ahmed
...and 1,214 more Authors
all top 5

Cited in 266 Serials

73 Journal of Functional Analysis
56 Proceedings of the American Mathematical Society
54 Probability Theory and Related Fields
52 Transactions of the American Mathematical Society
52 Statistics & Probability Letters
39 The Annals of Probability
36 Stochastic Processes and their Applications
35 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
34 Journal of Mathematical Analysis and Applications
29 Advances in Mathematics
24 Israel Journal of Mathematics
22 Mathematische Zeitschrift
21 Journal of Theoretical Probability
17 Potential Analysis
15 Sequential Analysis
13 Communications in Mathematical Physics
13 Illinois Journal of Mathematics
13 Mathematische Nachrichten
13 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
13 Bernoulli
13 The Journal of Fourier Analysis and Applications
12 Analysis Mathematica
12 Duke Mathematical Journal
12 Journal of Multivariate Analysis
12 Mathematische Annalen
12 Electronic Journal of Probability
11 Arkiv för Matematik
11 The Annals of Applied Probability
11 The Journal of Geometric Analysis
9 Acta Mathematica Hungarica
9 Revista Matemática Iberoamericana
9 Stochastic and Partial Differential Equations. Analysis and Computations
8 Studia Mathematica
8 Annales de l’Institut Fourier
8 Integral Equations and Operator Theory
8 Journal of Differential Equations
8 Stochastic Analysis and Applications
8 Bulletin of the American Mathematical Society
7 Journal of Approximation Theory
7 Tôhoku Mathematical Journal. Second Series
7 Electronic Communications in Probability
7 Comptes Rendus. Mathématique. Académie des Sciences, Paris
6 Lithuanian Mathematical Journal
6 Mathematical Proceedings of the Cambridge Philosophical Society
6 Rocky Mountain Journal of Mathematics
6 Bulletin of the American Mathematical Society. New Series
6 St. Petersburg Mathematical Journal
6 Positivity
6 Wuhan University Journal of Natural Sciences (WUJNS)
6 Mediterranean Journal of Mathematics
5 Journal d’Analyse Mathématique
5 Mathematical Methods in the Applied Sciences
5 Mathematical Notes
5 Annals of the Institute of Statistical Mathematics
5 Annali di Matematica Pura ed Applicata. Serie Quarta
5 Journal of Statistical Planning and Inference
5 Memoirs of the American Mathematical Society
5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
5 Siberian Mathematical Journal
5 Infinite Dimensional Analysis, Quantum Probability and Related Topics
5 Journal of Evolution Equations
5 Journal of Mathematical Inequalities
5 Science China. Mathematics
4 Acta Mathematica Academiae Scientiarum Hungaricae
4 Archive for Rational Mechanics and Analysis
4 Bulletin of the Australian Mathematical Society
4 Journal of Statistical Physics
4 Stochastics
4 Ukrainian Mathematical Journal
4 Theory of Probability and its Applications
4 Archiv der Mathematik
4 Journal of Soviet Mathematics
4 Monatshefte für Mathematik
4 Ergodic Theory and Dynamical Systems
4 Journal of the American Mathematical Society
4 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section B. Calcul des Probabilités et Statistique
4 Journal de Mathématiques Pures et Appliquées. Neuvième Série
4 Bulletin of the Polish Academy of Sciences, Mathematics
4 Stochastics
4 Banach Journal of Mathematical Analysis
3 The Canadian Journal of Statistics
3 Periodica Mathematica Hungarica
3 Acta Mathematica
3 The Annals of Statistics
3 Applied Mathematics and Optimization
3 Bulletin of the London Mathematical Society
3 Compositio Mathematica
3 Journal of Applied Probability
3 Journal of the London Mathematical Society. Second Series
3 Mathematika
3 Proceedings of the Japan Academy. Series A
3 Probability and Mathematical Statistics
3 Indagationes Mathematicae. New Series
3 Abstract and Applied Analysis
3 Journal of Inequalities and Applications
3 Annals of Mathematics. Second Series
3 Econometric Theory
3 Acta Mathematica Scientia. Series B. (English Edition)
3 Journal of Function Spaces and Applications
3 Journal of Statistical Theory and Practice
...and 166 more Serials
all top 5

Cited in 50 Fields

776 Probability theory and stochastic processes (60-XX)
333 Harmonic analysis on Euclidean spaces (42-XX)
285 Functional analysis (46-XX)
149 Operator theory (47-XX)
121 Partial differential equations (35-XX)
108 Statistics (62-XX)
61 Functions of a complex variable (30-XX)
45 Potential theory (31-XX)
36 Measure and integration (28-XX)
33 Numerical analysis (65-XX)
29 Dynamical systems and ergodic theory (37-XX)
27 Real functions (26-XX)
27 Ordinary differential equations (34-XX)
27 Abstract harmonic analysis (43-XX)
21 Integral transforms, operational calculus (44-XX)
18 Several complex variables and analytic spaces (32-XX)
18 Calculus of variations and optimal control; optimization (49-XX)
18 Statistical mechanics, structure of matter (82-XX)
17 Linear and multilinear algebra; matrix theory (15-XX)
15 Global analysis, analysis on manifolds (58-XX)
15 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
14 Fluid mechanics (76-XX)
13 Operations research, mathematical programming (90-XX)
11 Combinatorics (05-XX)
10 Biology and other natural sciences (92-XX)
9 Integral equations (45-XX)
8 Special functions (33-XX)
8 Systems theory; control (93-XX)
7 History and biography (01-XX)
7 Differential geometry (53-XX)
7 Quantum theory (81-XX)
7 Information and communication theory, circuits (94-XX)
6 Topological groups, Lie groups (22-XX)
6 Mechanics of deformable solids (74-XX)
5 Number theory (11-XX)
5 Approximations and expansions (41-XX)
4 Group theory and generalizations (20-XX)
4 Difference and functional equations (39-XX)
4 Convex and discrete geometry (52-XX)
4 General topology (54-XX)
3 General and overarching topics; collections (00-XX)
3 Sequences, series, summability (40-XX)
3 Computer science (68-XX)
3 Classical thermodynamics, heat transfer (80-XX)
2 Mathematical logic and foundations (03-XX)
2 Geometry (51-XX)
2 Mechanics of particles and systems (70-XX)
2 Geophysics (86-XX)
1 Nonassociative rings and algebras (17-XX)
1 Manifolds and cell complexes (57-XX)

Citations by Year

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