Weighted estimates for commutators of anisotropic Calderón-Zygmund operators

Abstract

Let T be an anisotropic Calderón-Zygmund operator and with and being an anisotropic weighted Lipschitz space. The goal of the paper is to give five boundedness theorems of the commutator . Precisely, is bounded from to , where , , and ; is bounded from to , when or , , and ; is bounded from anisotropic weighted Hardy space to , if or , and ; is bounded from to weak Lebesgue space with , , which are extensions of isotropic settings and new even for the isotropic weighted and anisotropic unweighted settings.