Characterizations of Mixed Herz-Hardy Spaces and their Applications

2022/05/20 by Yichun Zhao, Zhao, Yichun, Mingquan Wei +3
Mathematics · #Advanced Harmonic Analysis Research #advanced mathematical theories #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.2205.10372

Abstract

The purpose of this paper is to introduce and investigate some basic properties of mixed homogeneous Herz-Hardy spaces HK_p^{α, q}(ℝⁿ) and mixed non-homogeneous Herz-Hardy spaces HK_p^{α, q}(ℝⁿ). Furthermore, we establish the atom and molecular decompositions for HK_p^{α, q}(ℝⁿ) and HK_p^{α, q}(ℝⁿ), 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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