Selected Works of Donald L. Burkholder

On a class of stochastic approximation processes.- Sufficiency in the undominated case.- Iterates of conditional expectation operators.- On the order structure of the set of sufficient subfields.- Semi-Gaussian subspaces.- Successive conditional expectations of an integrable function.- Maximal inequalities as necessary conditions for almost everywhere convergence.- Martingale transforms. Ann. Math. Statist.- Extrapolation and interpolation of quasilinear operators on martingales.- A maximal function characterization of the class Hp.- Distribution function inequalities for the area integral.- Distribution function inequalities for martingales.- Boundary behaviour of harmonic functions in a half-space and Brownian motion.- One-sided maximal functions and Hp. J. Functional Analysis.- Boundary value estimation of the range of an analytic function.- A sharp inequality for martingale transforms.- Weak inequalities for exit times and analytic functions.- A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional.- Martingale transforms and the geometry of Banach spaces.- A nonlinear partial differential equation and the unconditional constant of the Haar system in Lp.- Boundary value problems and sharp inequalities for martingale transforms.- An elementary proof of an inequality of R. E. A. C. Paley.- Martingales and Fourier analysis in Banach spaces.- A sharp and strict Lp-inequality for stochastic integrals.- A proof of Pelczyn´ski's conjecture for the Haar system.- Differential subordination of harmonic functions and martingales.- Explorations in martingale theory and its applications.- Strong differential subordination and stochastic integration.- The best constant in the Davis inequality for the expectation of the martingale square function.- Joseph L. Doob.