Molecular Decomposition of Anisotropic Hardy Spaces With Variable Exponents

Abstract

Let A be an expansive dilation on ℝn, and p(·): ℝn → (0, ∞) be a variable exponent function satisfying the globally log-Holder continuous condition. Let \(H_A^{p\left(\cdot \right)}\left({{\mathbb{R}^n}} \right)\) be the variable anisotropic Hardy space defined via the non-tangential grand maximal function. In this paper, the authors establish its molecular decomposition, which is still new even in the classical isotropic setting (in the case A:= 2In×n). As applications, the authors obtain the boundedness of anisotropic Calderon-Zygmund operators from \(H_A^{p\left(\cdot \right)}\left({{\mathbb{R}^n}} \right)\) to Lp(·)(ℝn) or from \(H_A^{p\left(\cdot \right)}\left({{\mathbb{R}^n}} \right)\) to itself.