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arXiv · 2412.20773

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

Mickaël Latocca·Vincent Munnier
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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 $L^p$, 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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Mickaël Latocca, Vincent Munnier. 2024-12-30. Marcinkiewicz Type Theorems for Interpolation of Operators Acting on M{\"u}ntz Spaces. https://arxiv.org/abs/2412.20773

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