Transference in spaces of measures

Nakhlé Asmar; Stephen J. Montgomery-Smith; Sadahiro Saeki

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arXiv · math/9708204

Transference in spaces of measures

Nakhlé Asmar·Stephen J. Montgomery-Smith·Sadahiro Saeki

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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.

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BibTeX RIS

Nakhlé Asmar, Stephen J. Montgomery-Smith, Sadahiro Saeki. 1999-12-03. Transference in spaces of measures. https://arxiv.org/abs/math/9708204

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