Celebratio Mathematica — Burkholder

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Works connected to Maurizio Pratelli

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D. L. Burkholder: “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

The power of martingale theory in the study of the Fourier analysis of scalarvalued functions is now widely appreciated. Our aim here is to describe some new martingale methods and their application to the Fourier analysis of functions having values in a Banach space.

One of the themes of this work is that the new methods developed for B-valued martingales can be used to obtain new information even in the real case, for example, the best constants in some basic inequalities. These sharp inequalities for real-valued martingales lead, in turn, to new information about some of the classical Banach spaces, for example, the unconditional constant of any monotone basis of \( L^p(O,1) \) where \( 1 < p < \infty \).

Giorgio Letta	Related
Maurizio Pratelli	Related