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arXiv · 2605.20597

Atomic Characterization and Its Applications of Matrix-Weighted Variable Hardy Spaces

Yiqun Chen·Dachun Yang·Wen Yuan·Zongze Zeng
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Abstract

In this article, by means of the matrix-weighted grand maximal function we first introduce the variable Hardy space $H^{p(\cdot)}_W$ on $\mathbb{R}^n$ with the $\mathscr{A}_{p(\cdot),\infty}$ matrix weight $W$ and with the variable exponent $p(\cdot)$ having globally log-H\"older continuity, and then via using several different convex body valued maximal functions we establish its various maximal function equivalent characterizations. Combining a refined Whitney decomposition with both the convex body valued maximal function and its corresponding convex-body reducing operator, we obtain the atomic characterization of $H^{p(\cdot)}_W$. As applications, we give its dual space and establish the boundedness of Calder\'on--Zygmund operators from $H^{p(\cdot)}_W$ to the matrix-weighted variable Lebesgue space $L^{p(\cdot)}_W$ and to itself. This approach to establishing atomic characterization differs from all previous ones.

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BibTeXRIS

Yiqun Chen, Dachun Yang, Wen Yuan, Zongze Zeng. 2026-05-20. Atomic Characterization and Its Applications of Matrix-Weighted Variable Hardy Spaces. https://arxiv.org/abs/2605.20597

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