Revisiting mixed weak inequalities of Fefferman-Stein type for commutators of Calder\'on-Zygmund operators: an improvement

TL;DR

This paper improves existing mixed weak inequalities of Fefferman-Stein type for Calderón-Zygmund operators and their commutators, generalizing classical weighted weak inequalities through a novel measure-based approach.

Contribution

It introduces improved mixed weak inequalities for Calderón-Zygmund operators and commutators, extending classical results with a new measure-based method.

Findings

Enhanced inequalities for Calderón-Zygmund operators

Generalization of classical weighted weak Fefferman-Stein inequalities

New approach using measure-based inequalities

Abstract

In this paper we establish mixed weak inequalities of Fefferman-Stein type for Calder\'on-Zygmund operators and their commutators, improving some previous results known in the literature. The main estimates also generalize the classical weighted weak Fefferman-Stein inequalities proved in [19] and [22]. In order to obtain the main results, our approach is to give a strong Fefferman-Stein type inequality for the operators involved with respect to an adequate measure.