Commutators of Maximal Operator and Sharp Maximal Operator on Local Morrey-Lorentz Spaces

Abstract

In this paper, we study the boundedness of the maximal commutator operator Mb, the commutators of the maximal operator [b, M] and the commutators of the sharp maximal operator [b, M♯ ] in the local Morrey-Lorentz spaces Mp,q;λloc (ℝn). We give necessary and sufficient conditions for the boundedness of the operators Mb, [b, M] and [b, M♯ ] on local Morrey-Lorentz spaces Mp,q;λloc (ℝn) when b belongs to BMO(ℝn) spaces, whereby some new characterizations for certain subclasses of BMO(ℝn) spaces are obtained.