Characterizations of Mixed Herz-Hardy Spaces and their Applications

The purpose of this paper is to introduce and investigate some basic properties of mixed homogeneous Herz-Hardy spaces $H\dot{K}_{\vec{p}}^{α, q}(\mathbb{R}^n)$ and mixed non-homogeneous Herz-Hardy spaces $HK_{\vec{p}}^{α, q}(\mathbb{R}^n)$. Furthermore, we establish the atom and molecular decompositions for $H\dot{K}_{\vec{p}}^{α, q}(\mathbb{R}^n)$ and $HK_{\vec{p}}^{α, q}(\mathbb{R}^n)$, 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.

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