$M^2$-type sharp estimates and weighted boundedness for commutators related to singular integral operators satisfying a variant of Hörmander's condition

Abstract

In this paper, we prove the $M^k$-type sharp maximal function estimates for the commutators related to some singular integral operators satisfying a variant of Hörmander's condition.  As an application, we obtain the weighted boundedness of the commutators on Lebesgue and Morrey spaces.