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Don Burkholder’s work on Banach spaces

  • Burgess Davis
  • Renming Song
Chapter
Part of the Selected Works in Probability and Statistics book series (SWPS)

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.

Keywords

Banach Space Singular Integral Operator Fourier Multiplier Haar System Bellman Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematics and Department of StatisticsPurdue UniversityWest LafayetteUSA
  2. 2.Department of MathematicsUniversity of IllinoisUrbanaUSA

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