Local Morrey–Lorentz Spaces and Commutators of Fractional Maximal Operator with Lipschitz Functions on them

Abstract

In this paper, we give necessary and sufficient conditions for the boundedness of the fractional maximal commutator operator (Formula presented.) and the commutators of the fractional 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.