Transference in spaces of measures
Abstract
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.
Cite
@article{arxiv.math/9708204,
title = {Transference in spaces of measures},
author = {Nakhlé Asmar and Stephen J. Montgomery-Smith and Sadahiro Saeki},
journal= {arXiv preprint arXiv:math/9708204},
year = {2008}
}
Comments
Also available at http://www.math.missouri.edu/~stephen/preprints/