Commutators of maximal operator with Lipschitz functions on local Morrey-Lorentz spaces

In this paper, we give necessary and sufficient conditions for the boundedness of the maximal commutator operator (Formula presented.) and the commutators of the maximal operator (Formula presented.) in the local Morrey-Lorentz spaces (Formula presented.) when b belongs to Lipschitz spaces (Formula presented.), whereby some new characterizations for certain subclasses of (Formula presented.) spaces are obtained. © 2025 Elsevier B.V., All rights reserved.