$M^2$-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.

Keywords

• Singular integral operator
• Commutator
• Sharp maximal function
• Morrey space
• BMO