New function spaces of Morrey-Campanato type on spaces of homogeneous type

Abstract

In the context of spaces of homogeneous type, we introduce and develop some new function spaces of Morrey-Campanato type. The new function spaces are defined by variants of maximal functions associated with generalized approximations to the identity, and they generalize the classical Morrey-Campanato spaces. We show that the John-Nirenberg inequality holds on these spaces. We also establish the endpoint boundedness of fractional integrals.