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Don Burkholder’s work on Banach spaces

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Selected Works of Donald L. Burkholder

Part of the book series: Selected Works in Probability and Statistics ((SWPS))

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Abstract

Martingale theory and especially Burkholder’s work fascinated me right from the start. Mar- tingales were extremely popular when I started as a PhD student in Paris in late 1972. Of course they still are, but they were a particularly "hot topic" at the Paris VI probability seminar under the leadership of Jaques Neveu (and the monitoring of P.A. Meyer from Strasbourg). The papers [16] and [17] (as well as Garsia’s book) had appeared not long before and their impact was still visible. I remember vividly Neveu’s lectures on Burkholder’s inequalities and the iJ1-BMO duality. There was also intense interest for martingales within the Harmonic Analysis group in Orsay where Gundy made frequent visits and worked with Varopoulos. There, martingale came to the center stage through the links revealed with Harmonic functions, area integrals, the Fefferman Stein theory of H p-spaces, and so on. Meanwhile, the potential theory community had to face the shocking news that its subject was now also a part of probability theory.

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Authors and Affiliations

  1. Department of Mathematics and Department of Statistics, Purdue University, West Lafayette, IN, 47907-2068, USA

    Burgess Davis

  2. Department of Mathematics, University of Illinois, Urbana, IL, 61801, USA

    Renming Song

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Correspondence to Burgess Davis .

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  1. , Department of Mathematics and, Purdue University, N. University Street 150, West Lafayette, 47907-2068, Indiana, USA

    Burgess Davis

  2. , Department of Mathematics, University of Illinois, Urbana, W. Green St. 1409, Urbana, 61801, Illinois, USA

    Renming Song

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Davis, B., Song, R. (2011). Don Burkholder’s work on Banach spaces. In: Davis, B., Song, R. (eds) Selected Works of Donald L. Burkholder. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7245-3_2

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