A unified method for maximal truncated Calder\'on-Zygmund operators in general function spaces by sparse domination

TL;DR

This paper introduces a unified sparse domination approach for maximal truncated Calderón-Zygmund operators in various function spaces, providing simplified proofs and precise constant dependencies in weighted inequalities across Euclidean and homogeneous spaces.

Contribution

It offers a new, streamlined method for analyzing these operators in general function spaces, extending results to spaces of homogeneous type with explicit constant control.

Findings

Simplified proofs of key inequalities using sparse domination.

Results valid in Euclidean spaces and spaces of homogeneous type.

Explicit tracking of constants in weighted norm inequalities.

Abstract

In this note we give simple proofs of several results involving maximal truncated Calde\'on-Zygmund operators in the general setting of rearrangement invariant quasi-Banach function spaces by sparse domination. Our techniques allow us to track the dependence of the constants in weighted norm inequalities; additionally, our results hold in $\mathbb{R}^n$ as well as in many spaces of homogeneous type.