Commutators of the maximal function with BMO functions on total mixed Morrey spaces

In this paper, we introduce the total mixed Morrey spaces L p,, (R n ) and establish some basic properties and embeddings.We prove the boundedness of the maximal commutator operator M b and the commutator of the maximal operator [b, M ] on total mixed Morrey spaces L p,, (R n ).Using the boundedness results, we obtain some new characterizations for certain subclasses of the BM O(R n ) space.