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Characterizations of Mixed Herz-Hardy Spaces and their Applications (2205.10372v1)

Published 20 May 2022 in math.FA and math.CA

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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