Commutators of the Hardy-Littlewood Maximal Operator with BMO Symbols on Spaces of Homogeneous Type

Abstract

Weighted $L^p$ for $p\in (1,\infty )$ and weak-type endpoint estimates with general weights are established for commutators of the Hardy-Littlewood maximal operator with BMO symbols on spaces of homogeneous type. As an application, a weighted weak-type endpoint estimate is proved for maximal operators associated with commutators of singular integral operators with BMO symbols on spaces of homogeneous type. All results with no weight on spaces of homogeneous type are also new.