Characterizations of Mixed Herz-Hardy Spaces and their Applications

Abstract

The purpose of this paper is to introduce and investigate some basic properties of mixed homogeneous Herz-Hardy spaces $H{\dot{K}}_{\vec{p}}^{\alpha ,q}({\mathbb{R}}^n)$ and mixed non-homogeneous Herz-Hardy spaces $H{K}_{\vec{p}}^{\alpha ,q}({\mathbb{R}}^n)$. Furthermore, we establish the atom and molecular decompositions for $H{\dot{K}}_{\vec{p}}^{\alpha ,q}({\mathbb{R}}^n)$ and $H{K}_{\vec{p}}^{\alpha ,q}({\mathbb{R}}^n)$, by which the boundedness for a wide class of sublinear operators on mixed Herz-Hardy spaces is obtained. As a byproduct, the dual spaces of mixed homogeneous Herz-Hardy spaces are deduced.