A note on the Coifman-Fefferman and Fefferman-Stein inequalities

TL;DR

This paper explores conditions on Banach function spaces that make the Coifman-Fefferman and Fefferman-Stein inequalities equivalent, clarifying their relationship in harmonic analysis.

Contribution

It provides a specific condition on Banach function spaces under which these two fundamental inequalities are equivalent, advancing theoretical understanding.

Findings

Identifies a condition on Banach spaces for inequality equivalence

Clarifies the relationship between Coifman-Fefferman and Fefferman-Stein inequalities

Enhances theoretical framework in harmonic analysis

Abstract

A condition on a Banach function space $X$ is given under which the Coifman-Fefferman and Fefferman-Stein inequalities on $X$ are equivalent.