Maximal commutator and commutator of maximal function on total Morrey spaces

Abstract

In this paper we introduce a new variant of Morrey spaces called total Morrey spaces L p, , (R n ) .These spaces generalize the classical Morrey spaces so that L p, , (R n ) L p, (R n ) and the modified Morrey spaces so that L p, ,0 (R n ) = L p, (R n ) .We give basic properties of the spaces L p, , (R n ) and study some embeddings into the Morrey space L p, , (R n ) .We also give necessary and sufficient conditions for the boundedness of the maximal commutator operator M b and commutator of maximal operator [b,M] on L p, , (R n ) .We obtain some new characterizations for certain subclasses of BMO(R n ) .

Topics & Concepts