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Extrapolation and Interpolation of Quasi-Linear Operators on Martingales

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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

In this paper we introduce a new method to obtain one-sided and two-sided integral inequalities for a class of quasi-linear operators. Some of our assumptions are similar to those of the Marcinkiewicz interpolation theorem. However, in contrast to the Marcinkiewicz theorem, the operators that we study here are local in a certain sense and are usually most conveniently defined on martingales. In fact, the suitable choice of starting and stopping times for martingales, together with the systematic use of maximal functions and maximal operators, is central to our method.

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Author information

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

Authors
  1. Burgess Davis
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  2. Renming Song
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Correspondence to Burgess Davis .

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Editors and Affiliations

  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). Extrapolation and Interpolation of Quasi-Linear Operators on Martingales. 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_11

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