Atomic Characterization and Its Applications of Matrix-Weighted Variable Hardy Spaces
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
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2026
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| _version_ | 1866918520754798592 |
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| author | Chen, Yiqun Yang, Dachun Yuan, Wen Zeng, Zongze |
| author_facet | Chen, Yiqun Yang, Dachun Yuan, Wen Zeng, Zongze |
| contents | 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-Hölder 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 Calderón--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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20597 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Atomic Characterization and Its Applications of Matrix-Weighted Variable Hardy Spaces Chen, Yiqun Yang, Dachun Yuan, Wen Zeng, Zongze Functional Analysis Analysis of PDEs Classical Analysis and ODEs Primary 42B30, Secondary 42B25, 42B20, 47A56, 46E40, 46E35, 42B35 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-Hölder 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 Calderón--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. |
| title | Atomic Characterization and Its Applications of Matrix-Weighted Variable Hardy Spaces |
| topic | Functional Analysis Analysis of PDEs Classical Analysis and ODEs Primary 42B30, Secondary 42B25, 42B20, 47A56, 46E40, 46E35, 42B35 |
| url | https://arxiv.org/abs/2605.20597 |