Lusin Area Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces and Their Applications

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Lusin Area Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces and Their ApplicationsLet φ: Rⁿ× [0,∞)→[0,∞) be a growth function such that φ(x,·) is nondecreasing, φ(x,0)=0, φ(x,t)>0 when t>0, ₜ→∞φ(x,t)=∞, and φ(·,t) is a Muckenhoupt A∞(Rⁿ) weight uniformly in t. In this paper, the authors establish the Lusin area function and the molecular characterizations of the Musielak-Orlicz Hardy space Hφ(Rⁿ) introduced by Luong Dang Ky via the grand maximal function. As an application, the authors obtain the φ-Carleson measure characterization of the Musielak-Orlicz -type space φ(Rⁿ), which was proved to be the dual space of Hφ(Rⁿ) by Luong Dang Ky.