REAL-VARIABLE CHARACTERIZATIONS OF MUSIELAK ORLICZ HARDY SPACES ON SPACES OF HOMOGENEOUS TYPE

摘要

Let (X,d,μ)be a space of homogeneous type in the sense ofCoifman and Weiss. In this article, the authors establisha complete real-variable theory of Musielak-Orlicz Hardy spaceson (X,d,μ).To be precise, the authors first introduce the atomic Musielak-Orlicz Hardy spaceH at(X) andthen establish its various maximal function characterizations.The authors also investigate the Littlewood-Paley characterizationsof H at(X) viaLusin area functions, Littlewood-Paley g-functionsand Littlewood-Paley g -functions.The authors further obtain the finite atomic characterization ofH at(X) and itsimproved version in case q H at(X) to a quasi-Banach space,which are also applied to the boundedness of Caldern-Zygmund operators.Moreover, the authors find the dual space of H at(X),namely, the Musielak-Orlicz BMOspace BMO (X), present its severalequivalent characterizations,and apply it to establish a new characterization of the set of pointwise multipliersfor the space BMO(X).The main novelty of this article is that, throughout the article, except the last section,μ is not assumed to satisfy the reverse doubling condition.