Marcinkiewicz Type Theorems for Interpolation of Operators Acting on Müntz Spaces

2024/12/30 by Mickaël Latocca, Latocca, Mickaël, Vincent Munnier +1
Mathematics · #Approximation Theory and Sequence Spaces #Advanced Banach Space Theory #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2412.20773

Abstract

We prove interpolation results in the spirit of the Marcinkiewicz theorem. The operators considered in this article are defined on Müntz spaces, which are not dense subspaces of L^p, and for which the classical interpolation theory cannot be applied directly. Our proofs crucially rely on strong decoupling of L^p norms, a that was first observed by Gurariy-Macaev and later generalized.

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