A characterization of the weighted weak type Coifman-Fefferman and Fefferman-Stein inequalities

TL;DR

This paper introduces a new condition called $SC_p$ that characterizes weighted weak type inequalities related to classical harmonic analysis results, providing a deeper understanding of these inequalities.

Contribution

The paper presents the $SC_p$ condition as a novel characterization of weighted weak type Coifman-Fefferman and Fefferman-Stein inequalities, expanding theoretical understanding.

Findings

$SC_p$ condition characterizes weighted weak type inequalities

Provides a new framework for understanding classical inequalities

Enhances theoretical tools in harmonic analysis

Abstract

We introduce a variant of the $C_p$ condition (denoted by $SC_p$), and show that it characterizes weighted weak type versions of the classical Coifman-Fefferman and Fefferman-Stein inequalities.