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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2510.05924 |
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| _version_ | 1866912633184059392 |
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| author | Liu, Xiong Wang, Wenhua |
| author_facet | Liu, Xiong Wang, Wenhua |
| contents | Let $α\in\mathbb{R}$, $p\in[1,\infty)$, $q\in(0,\infty]$, $\mathbf{W}$ be a matrix weight, and $A$ be an expansive dilation on $\mathbb{R}^d$. In this paper, the authors firstly investigate and develop some aspects of homogeneous anisotropic Besov spaces $\dot{B}^{α,q}_{p,A}(\mathbb{R}^d,\mathbf{W})$ and inhomogeneous anisotropic Besov spaces $B^{α,q}_{p,A}(\mathbb{R}^d,\mathbf{W})$ theory in the matrix weight setting. Moreover, we show that these spaces are characterized by the magnitude of the $φ$-transforms in appropriate sequence spaces. Notably, all these results remain novel even in the diagonal non-isotropic case (when $A = \mathrm{diag}(λ_1, λ_2, \ldots, λ_d)$ with $\{λ_j\}_{j=1}^d \subset \mathbb{C}$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05924 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matrix-Weighted Besov Spaces Associated with Non-isotropic Dilations Liu, Xiong Wang, Wenhua Functional Analysis 42B25, 42B35, 47B38 Let $α\in\mathbb{R}$, $p\in[1,\infty)$, $q\in(0,\infty]$, $\mathbf{W}$ be a matrix weight, and $A$ be an expansive dilation on $\mathbb{R}^d$. In this paper, the authors firstly investigate and develop some aspects of homogeneous anisotropic Besov spaces $\dot{B}^{α,q}_{p,A}(\mathbb{R}^d,\mathbf{W})$ and inhomogeneous anisotropic Besov spaces $B^{α,q}_{p,A}(\mathbb{R}^d,\mathbf{W})$ theory in the matrix weight setting. Moreover, we show that these spaces are characterized by the magnitude of the $φ$-transforms in appropriate sequence spaces. Notably, all these results remain novel even in the diagonal non-isotropic case (when $A = \mathrm{diag}(λ_1, λ_2, \ldots, λ_d)$ with $\{λ_j\}_{j=1}^d \subset \mathbb{C}$). |
| title | Matrix-Weighted Besov Spaces Associated with Non-isotropic Dilations |
| topic | Functional Analysis 42B25, 42B35, 47B38 |
| url | https://arxiv.org/abs/2510.05924 |