MAXIMAL COMMUTATOR AND COMMUTATOR OF MAXIMAL FUNCTION ON TOTAL MORREY SPACES

In this paper we introduce a new variant of Morrey spaces called total Morrey spaces(formula present). These spaces generalize the classical Morrey spaces so that(formula present) and the modified Morrey spaces so that(formula present). We give basic properties of the spaces (formula present) and study some embeddings into the Morrey space (formula present). We also give necessary and sufficient conditions for the boundedness of the maximal commutator operator Mb and commutator of maximal operator [b,M] on (formula present). We obtain some new characterizations for certain subclasses of BMO(formula present). © 2022,Journal of Mathematical Inequalities.All Rights Reserved.