Let \((\cal{X},d,\mu)\) be a space of homogeneous type, in the sense of Coifman and Weiss, and \(\varphi:\cal{X}\times[0,\infty)\rightarrow[0,\infty)\) satisfy that, for almost every \(x\in\cal{X},\varphi(x,\cdot)\) is an Orlicz function and that φ(·, t) is a Muckenhoupt \(\mathbb{A}_{\infty}(\cal{X})\) weight uniformly in t ∈ [0, ∞). In this article, the authors first establish a new molecular characterization, associated with admissible sequences of balls on \(\cal{X}\) , of the Musielak-Orlicz Hardy space \(H^{\varphi}(\cal{X})\) . As an application, the authors also obtain the boundedness of Calderón-Zygmund operators from \(H^{\varphi}(\cal{X})\) to \(H^{\varphi}(\cal{X})\) or to the Musielak-Orlicz space \(L^{\varphi}(\cal{X})\) . The main novelty of these results is that, in the proof of the boundedness of Calderón-Zygmund operators on \(H^{\varphi}(\cal{X})\) , the authors get rid of the dependence on the reverse doubling property of μ by using this new molecular characterization of \(H^{\varphi}(\cal{X})\) .
