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arXiv · 2205.10372

Characterizations of Mixed Herz-Hardy Spaces and their Applications

Yichun Zhao·Mingquan Wei·Jiang Zhou
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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.

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Yichun Zhao, Mingquan Wei, Jiang Zhou. 2022-05-20. Characterizations of Mixed Herz-Hardy Spaces and their Applications. https://arxiv.org/abs/2205.10372

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