New Molecular Characterization of Musielak-Orlicz Hardy Spaces on Spaces of Homogeneous Type and Its Applications

Let （X,d,μ） be a space of homogeneous type,in the sense of Coifman and Weiss,andφ:X×[0,∞)→[0,∞) satisfy that,for almost every x∈X,φ（x,·） is an Orlicz function and thatφ（·,t） is a Muckenhoupt A∞（X） weight uniformly in t∈[0,∞).In this article,the authors first establish a new molecular characterization,associated with admissible sequences of balls on X,of the Musielak-Orlicz Hardy space Hφ（X）.As an application,the authors also obtain the boundedness of Calderón-Zygmund operators from Hφ（X） to Hφ（X） or to the Musielak-Orlicz space Lφ（X）.The main novelty of these results is that,in the proof of the boundedness of Calderón-Zygmund operators on Hφ（X）,the authors get rid of the dependence on the reverse doubling property ofμby using this new molecular characterization of Hφ（X）.