Marcinkiewicz Type Theorems for Interpolation of Operators Acting on M{ü}ntz Spaces

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.