Commutators of Anisotropic Maximal Operators with BMO Functions on Anisotropic Total Morrey Spaces

In this paper we consider the anisotropic maximal commutator M d b and the commutator of the anisotropic maximal operator [b, M d ] on the anisotropic total Morrey spaces L d p,, (R n ).We obtain necessary and sufficient conditions for the boundedness of the operators M d b and [b, M d ] on L d p,, (R n ) when b belongs to the bounded mean oscillation space BM O(R n ).We also obtain new characterizations for some subclasses of BM O(R n ).