Regularity of Commutators of Maximal Operators with Lipschitz Symbols

Abstract

This paper is devoted to studying Sobolev regularity properties of commutators of Hardy-Littlewood maximal operator and its fractional case with Lipschitz symbols, both in the global and local case. Some new pointwise estimates for the weak gradients of the above commutators will be established. As applications, some bounds for the above commutators on the Sobolev spaces will be obtained.