Caractérisation des espaces de Lipschitz via les commutateurs de l'opérateur maximal de Hardy–Littlewood

Abstract

Let M be the Hardy–Littlewood maximal function and b be a locally integrable function. Denote by Mb and [b,M] the maximal commutator and the (nonlinear) commutator of M with b. In this paper, the author considers the boundedness of Mb and [b,M] on Lebesgue spaces and Morrey spaces when b belongs to the Lipschitz space, by which some new characterizations of the Lipschitz spaces are given.