Molecular characterization of anisotropic weak Musielak-Orlicz Hardy spaces and their applications

Abstract

Let A be a real n × n matrix with all its eigenvalues λ satisfy |λ| > 1. Let ϕ : R n × [0, ∞) → [0, ∞) be an anisotropic Musielak-Orlicz function, i.e., ϕ(x, •) is an Orlicz function uniformly in x ∈ R n and ϕ(•, t) is an anisotropic Muckenhoupt A∞(R n) weight uniformly in t ∈ (0, ∞). In this article, the authors introduce the anisotropic weak Musielak-Orlicz Hardy space W H ϕ A (R n) via the grand maximal function and establish its molecular characterization which are anisotropic extensions of Liang, Yang and Jiang (Math. Nachr. 289: 634-677, 2016). As an application, the boundedness of anisotropic Calderón-Zygmund operators from H ϕ A (R n) to W H ϕ A (R n) in the critical case is presented.