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Extrapolation and Interpolation of Quasi-Linear Operators on Martingales

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

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.

Keywords

Positive Real Number Maximal Function Difference Sequence Integral Inequality Matrix Type 
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Copyright information

© 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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