Commutators of the Maximal Function with BMO Functions on Total Mixed Morrey Spaces

Abstract

In this paper, we introduce the total mixed Morrey spaces L⃗p,λ,µ(ℝn) and establish some basic properties and embeddings. We prove the boundedness of the maximal commutator operator Mb and the commutator of the maximal operator [b, M] on total mixed Morrey spaces L⃗p,λ,µ(ℝn). Using the boundedness results, we obtain some new characterizations for certain subclasses of the BMO(ℝn) space.