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 L-p,L-lambda,L-mu(R-n). These spaces generalize the classical Morrey spaces so that L-p,L-lambda,L-lambda (R-n) equivalent to L-p,L-lambda(R-n) and the modified Morrey spaces so that L-p,L-lambda,L-0(R-n) = (L) over tilde (p,lambda) (R-n). We give basic properties of the spaces L-p,L-lambda,L-lambda(R-n) and study some embeddings into the Morrey space L-p,L-lambda,L-mu (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,L-lambda,L-mu(R-n). We obtain some new characterizations for certain subclasses of BMO(R-n).