Extrapolation of compactness on weighted Morrey spaces

TL;DR

This paper extends weighted extrapolation theorems to weighted Morrey spaces, enabling the transfer of compactness properties of operators from one space to a range of spaces, with applications to singular integrals.

Contribution

It generalizes previous weighted extrapolation results to Morrey spaces, providing new tools for analyzing operator compactness in these settings.

Findings

Extended weighted extrapolation to Morrey spaces.

Established weighted compactness of commutators of singular integrals.

Derived new results on Bochner--Riesz multipliers.

Abstract

In a previous work, "compact versions" of Rubio de Francia's weighted extrapolation theorem were proved, which allow one to extrapolate the compactness of an linear operator from just one space to the full range of weighted Lebesgue spaces, where this operator is bounded. In this paper, we extend these results to the setting of weighted Morrey spaces. As applications, we easily obtain new results on the weighted compactness of commutators of Calder\'on--Zygmund singular integrals, rough singular integrals and Bochner--Riesz multipliers.