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 $HK{\vec{p}}^{\alpha, q}(\mathbb{R}^n)$. Furthermore, we establish the atom and molecular decompositions for $H\dot{K}{\vec{p}}^{\alpha, q}(\mathbb{R}^n)$ and $HK{\vec{p}}^{\alpha, q}(\mathbb{R}^n)$, 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.