The boundedness for commutators of maximal hypersingular integrals with rough kernels

Abstract

In this paper, we prove that the commutators of maximal hypersingular integrals with rough kernels are bounded from the Sobolev space \(\dot L_\gamma ^p \left( {\mathbb{R}^n } \right)\) to the Lebesgue space L p (ℝ n ), which is a substantial improvement and an extension of some known results.