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

摘要

Let phi : x [0, co)-4 [0, infinity) -> [0, infinity) be an anisotropic growth function and A a general expansive matrix on R". Let H-A(phi)(R-n) 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 H-A(phi) (R-n) 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 H-A(phi) (R-n), which further implies the boundedness of integral anisotropic Calderon-Zygmund operators on H-A(phi) (R-n). In addition, the boundedness of these operators from H-A(phi) (R-n) to the Musielak-Orlicz space L-phi (R-n) is also presented. (C) 2019 Elsevier Inc. All rights reserved.