Fock projections on vector-valued $L^p$-spaces with matrix weights
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908610408218624 |
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| author | Chen, Jiale Wang, Maofa |
| author_facet | Chen, Jiale Wang, Maofa |
| contents | In this paper, we characterize the $d\times d$ matrix weights $W$ on $\mathbb{C}^n$ such that the Fock projection $P_α$ is bounded on the vector-valued spaces $L^p_{α,W}(\mathbb{C}^n;\mathbb{C}^d)$ induced by $W$ and the Gaussian measures. It is proved that for $1\leq p\leq\infty$, the Fock projection $P_α$ is bounded on $L^p_{α,W}(\mathbb{C}^n;\mathbb{C}^d)$ if and only if $W$ satisfies a restricted $\mathcal{A}_p$-condition. Our result is new even in the scalar setting at the endpoint $p=\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13537 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fock projections on vector-valued $L^p$-spaces with matrix weights Chen, Jiale Wang, Maofa Functional Analysis In this paper, we characterize the $d\times d$ matrix weights $W$ on $\mathbb{C}^n$ such that the Fock projection $P_α$ is bounded on the vector-valued spaces $L^p_{α,W}(\mathbb{C}^n;\mathbb{C}^d)$ induced by $W$ and the Gaussian measures. It is proved that for $1\leq p\leq\infty$, the Fock projection $P_α$ is bounded on $L^p_{α,W}(\mathbb{C}^n;\mathbb{C}^d)$ if and only if $W$ satisfies a restricted $\mathcal{A}_p$-condition. Our result is new even in the scalar setting at the endpoint $p=\infty$. |
| title | Fock projections on vector-valued $L^p$-spaces with matrix weights |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2408.13537 |