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

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.