Transference in spaces of measures

Details Transference in spaces of measures Transference in spaces of measures

1997-08-04

arxiv.org/abs/math/9708204v2

J. Functional Analysis 165, (1999), 1-23

Mathematics

Functional Analysis

Also available at http://www.math.missouri.edu/~stephen/preprints/

Scientific paper

The transference theory for Lp spaces of Calderon, Coifman, and Weiss is a powerful tool with many applications to singular integrals, ergodic theory, and spectral theory of operators. Transference methods afford a unified approach to many problems in diverse areas, which before were proved by a variety of methods. The purpose of this paper is to bring about a similar approach to the study of measures. Specifically, deep results in classical harmonic analysis and ergodic theory, due to Bochner, de Leeuw-Glicksberg, Forelli, and others, are all extensions of the classical F.&M. Riesz Theorem. We will show that all these extensions are obtainable via our new transference principle for spaces of measures.

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