Matrix-Weighted Campanato Spaces: Duality and Calderón--Zygmund Operators
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915454562336768 |
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| author | Chen, Yiqun Yang, Dachun Yuan, Wen |
| author_facet | Chen, Yiqun Yang, Dachun Yuan, Wen |
| contents | Let $p\in(0,\infty)$, $q\in[1,\infty)$, $s\in\mathbb Z_+$, and $W$ be an $A_p$-matrix weight, which in the scalar case is exactly a Muckenhoupt $A_{\max\{1,p\}}$ weight. In this article, by using the reducing operators of $W$, we introduce matrix-weighted Campanato spaces $\mathcal L_{p,q,s,W}$. When $p\in(0,1]$, applying the atomic and the finite atomic characterizations of the matrix-weighted Hardy space $H^p_W$, we prove that the dual space of $H^p_W$ is precisely $\mathcal L_{p,q,s,W}$, which further induces several equivalent characterizations of $\mathcal L_{p,q,s,W}$. In addition, we obtain a necessary and sufficient condition for the boundedness of modified Calderón--Zygmund operators on $\mathcal L_{p,q,s,W}$ with $p\in(0,\infty)$, which, combined with the duality, further gives a necessary and sufficient condition for the boundedness of Calderón--Zygmund operators on $H^p_W$ with $p\in(0,1]$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_15195 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matrix-Weighted Campanato Spaces: Duality and Calderón--Zygmund Operators Chen, Yiqun Yang, Dachun Yuan, Wen Functional Analysis Analysis of PDEs Classical Analysis and ODEs Primary 46E35, Secondary 42B20, 42B30, 42B35, 46E40, 47A56 Let $p\in(0,\infty)$, $q\in[1,\infty)$, $s\in\mathbb Z_+$, and $W$ be an $A_p$-matrix weight, which in the scalar case is exactly a Muckenhoupt $A_{\max\{1,p\}}$ weight. In this article, by using the reducing operators of $W$, we introduce matrix-weighted Campanato spaces $\mathcal L_{p,q,s,W}$. When $p\in(0,1]$, applying the atomic and the finite atomic characterizations of the matrix-weighted Hardy space $H^p_W$, we prove that the dual space of $H^p_W$ is precisely $\mathcal L_{p,q,s,W}$, which further induces several equivalent characterizations of $\mathcal L_{p,q,s,W}$. In addition, we obtain a necessary and sufficient condition for the boundedness of modified Calderón--Zygmund operators on $\mathcal L_{p,q,s,W}$ with $p\in(0,\infty)$, which, combined with the duality, further gives a necessary and sufficient condition for the boundedness of Calderón--Zygmund operators on $H^p_W$ with $p\in(0,1]$. |
| title | Matrix-Weighted Campanato Spaces: Duality and Calderón--Zygmund Operators |
| topic | Functional Analysis Analysis of PDEs Classical Analysis and ODEs Primary 46E35, Secondary 42B20, 42B30, 42B35, 46E40, 47A56 |
| url | https://arxiv.org/abs/2508.15195 |