A new $A_p$-$A_\infty$ estimate for Calder\'on-Zygmund operators in spaces of homogeneous type

TL;DR

This paper establishes a novel $A_p$-$A_ Infty$ estimate for Calderón-Zygmund operators using weak $A_ Infty$ characteristics, applicable in spaces of homogeneous type and even new in Euclidean space.

Contribution

It introduces a new $A_p$-$A_ Infty$ estimate for Calderón-Zygmund operators based on weak $A_ Infty$ characteristics, extending previous results.

Findings

New estimate in spaces of homogeneous type

Applicable to Euclidean space, even if previously unknown

Utilizes weak $A_ Infty$ class introduced by Anderson, Hytönen, and Tapiola

Abstract

In this note, we study the $A_p$-$A_\infty$ estimate for Calder\'on-Zygmund operators in terms of the weak $A_\infty$ characteristics in spaces of homogeneous type. The weak $A_\infty$ class was introduced recently by Anderson, Hyt\"onen and Tapiola. Our estimate is new even in the Euclidean space.