Nakhlé Asmar, Stephen Montgomery-Smith and Sadahiro Saeki, Transference in Spaces of Measures.
J. Functional Analysis 165, (1999), 1-23.
The transference theory for \(L^p\) 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.
List of all preprints