A new $A_p$-$A_{\infty }$ estimate for Calderón-Zygmund operators in spaces of homogeneous type

Abstract

In this note, we study the $A_p$-$A_{\infty }$ estimate for Calderón-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, Hytönen and Tapiola. Our estimate is new even in the Euclidean space.