English

Marcinkiewicz Type Theorems for Interpolation of Operators Acting on M{\"u}ntz Spaces

Functional Analysis 2024-12-31 v1

Abstract

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

Keywords

Cite

@article{arxiv.2412.20773,
  title  = {Marcinkiewicz Type Theorems for Interpolation of Operators Acting on M{\"u}ntz Spaces},
  author = {Mickaël Latocca and Vincent Munnier},
  journal= {arXiv preprint arXiv:2412.20773},
  year   = {2024}
}