Molecular Decomposition of Anisotropic Hardy Spaces with Variable Exponents

Abstract

Let $A$ be an expansive dilation on ${\mathbb{R}}^n$, and $p(\cdot ):{\mathbb{R}}^n\to (0,\infty )$ be a variable exponent function satisfying the globally log-Hölder continuous condition. Let $H_A^{p(\cdot )}({\mathbb{R}}^n)$ 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 $A:=2{\mathrm{I}}_{n\times n}$). As applications, the authors obtain the boundedness of anisotropic Calderón-Zygmund operators from $H_A^{p(\cdot )}({\mathbb{R}}^n)$ to $L^{p(\cdot )}({\mathbb{R}}^n)$ or from $H_A^{p(\cdot )}({\mathbb{R}}^n)$ to itself.

23 Pages. arXiv admin note: text overlap with arXiv:1705.05188 by other authors