Lorentz Boundedness Characterization of Commutators of Maximal Operators on Spaces of Homogeneous Type

Abstract

We study the Lorentz boundedness properties of the maximal commutator operator Mb on the space of homogeneous type and relate this property to spaces of bounded mean oscillations. We also study the Lorentz boundedness properties of the commutators of the maximal operator [b,M] and the commutators of the sharp maximal operator [b,M♯ ] on the space of homogeneous type and relate this property for certain subclasses of spaces of bounded mean oscillations.