Characterizations of Anisotropic Lipschitz Functions Via the Commutators of Anisotropic Maximal Function in Lorentz Spaces

Abstract

In this paper, we study the anisotropic maximal commutator (Formula presented.) and the commutator of the anisotropic maximal operator (Formula presented.) in the Lorentz spaces (Formula presented.). We obtain necessary and sufficient conditions for the boundedness of the operators (Formula presented.) and (Formula presented.) on the Lorentz spaces (Formula presented.) when b belongs to anisotropic Lipschitz spaces (Formula presented.). We obtain some new characterizations for certain subclasses of (Formula presented.).