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

Abstract

We shall give necessary and sufficient conditions for the boundedness of the anisotropic maximal commutators Mbd and the commutators of the anisotropic maximal operator[b, Md] in total Morrey spaces Ldp,λ,µ(Rn) when b belongs to anisotropic Lipschitz spaces Λ˙β,d(Rn), whereby some new characterizations for certain subclasses of anisotropic Lipschitz spaces Λ˙β,d(Rn) are obtained. © 2025, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. All rights reserved.