Matrix $A_p$-weights relative to a pseudo-metric
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908574484004864 |
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| author | Nielsen, Morten |
| author_facet | Nielsen, Morten |
| contents | Matrix weights satisfying a Muckenhoupt $A_p$-condition relative to a family of anisotropic balls in $\mathbb{R}^d$ defined by a pseudo-metric are studied. It is shown that such matrix weights satisfy a doubling condition and a reverse Hölder inequality. In the special case, where the pseudo-metric is homogeneous with respect to a one-parameter dilation group, the corresponding Muckenhoupt class is shows to satisfy an invariance property under composition with affine transformations generated by the dilation group. A general sampling theorem is derived for the matrix-weighted space $L^p(W)$ for Muckenhoupt $A_p$ weights $W$ along with a corresponding multiplier result for $L^p(W)$. An application of the results to the study of anisotropic matrix-weighed Besov spaces is considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matrix $A_p$-weights relative to a pseudo-metric Nielsen, Morten Functional Analysis Primary 42B15, 42B35, 46E36, Secondary 46E40 Matrix weights satisfying a Muckenhoupt $A_p$-condition relative to a family of anisotropic balls in $\mathbb{R}^d$ defined by a pseudo-metric are studied. It is shown that such matrix weights satisfy a doubling condition and a reverse Hölder inequality. In the special case, where the pseudo-metric is homogeneous with respect to a one-parameter dilation group, the corresponding Muckenhoupt class is shows to satisfy an invariance property under composition with affine transformations generated by the dilation group. A general sampling theorem is derived for the matrix-weighted space $L^p(W)$ for Muckenhoupt $A_p$ weights $W$ along with a corresponding multiplier result for $L^p(W)$. An application of the results to the study of anisotropic matrix-weighed Besov spaces is considered. |
| title | Matrix $A_p$-weights relative to a pseudo-metric |
| topic | Functional Analysis Primary 42B15, 42B35, 46E36, Secondary 46E40 |
| url | https://arxiv.org/abs/2510.02849 |