Endpoint estimates for compact Calder\'on-Zygmund operators

TL;DR

This paper establishes precise conditions under which Calderón-Zygmund operators are compact at the endpoint from L^1 to weak L^1, enhancing understanding of their boundary behavior in harmonic analysis.

Contribution

It provides necessary and sufficient criteria for the compactness of Calderón-Zygmund operators at the endpoint from L^1 to weak L^1, a key aspect in harmonic analysis.

Findings

Characterization of compactness conditions at the endpoint

Necessary and sufficient conditions established

Improved understanding of boundary behavior of operators

Abstract

We prove necessary and sufficient conditions for a Calder\'on-Zygmund operator to be compact at the endpoint from $L^{1}(\mathbb R^{d})$ into $L^{1,\infty}(\mathbb R^{d})$.