New molecular characterizations of anisotropic Musielak–Orlicz Hardy spaces and their applications

Abstract

Let φ:Rn×[0,∞)→[0,∞) be an anisotropic growth function and A a general expansive matrix on Rn. Let HAφ(Rn) be the anisotropic Musielak–Orlicz Hardy space associated with A defined via the non-tangential grand maximal function. In this article, the authors establish a new molecular characterization of HAφ(Rn) via its known atomic characterizations, which positively answer a question mentioned by Li et al. (2016) [34]. As an application, the authors obtain a criterion on the boundedness of linear operators on HAφ(Rn), which further implies the boundedness of integral anisotropic Calderón–Zygmund operators on HAφ(Rn). In addition, the boundedness of these operators from HAφ(Rn) to the Musielak–Orlicz space Lφ(Rn) is also presented.