Some characterizations of Lipschitz spaces via commutators of the Hardy-Littlewood maximal operator on slice spaces

Abstract

Let M be the Hardy-Littlewood maximal operator and b be a locally integrable function. Denote by M_b and [b,M] the maximal commutator and the nonlinear commutator of M with b. In this paper, we give necessary and sufficient conditions for the boundedness of M_b and [b,M] on slice spaces when the function b belongs to Lipschitz spaces, by which a new characterization of non-negative Lipschitz functions is obtained.