Absolutely summing Carleson embeddings on weighted Fock spaces with $A_{\infty}$-type weights
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916751171649536 |
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| author | Chen, Jiale He, Bo Wang, Maofa |
| author_facet | Chen, Jiale He, Bo Wang, Maofa |
| contents | In this paper, we investigate the $r$-summing Carleson embeddings on weighted Fock spaces $F^p_{α,w}$. By using duality arguments, translating techniques and block diagonal operator skills, we completely characterize the $r$-summability of the natural embeddings $I_d:F^p_{α,w}\to L^p_α(μ)$ for any $r\geq1$ and $p>1$, where $w$ is a weight on the complex plane $\mathbb{C}$ that satisfies an $A_p$-type condition. As applications, we establish some results on the $r$-summability of differentiation and integration operators, Volterra-type operators and composition operators. Especially, we completely characterize the boundedness of Volterra-type operators and composition operators on vector-valued Fock spaces for all $1<p<\infty$, which were left open before for the case $1<p<2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16109 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Absolutely summing Carleson embeddings on weighted Fock spaces with $A_{\infty}$-type weights Chen, Jiale He, Bo Wang, Maofa Functional Analysis In this paper, we investigate the $r$-summing Carleson embeddings on weighted Fock spaces $F^p_{α,w}$. By using duality arguments, translating techniques and block diagonal operator skills, we completely characterize the $r$-summability of the natural embeddings $I_d:F^p_{α,w}\to L^p_α(μ)$ for any $r\geq1$ and $p>1$, where $w$ is a weight on the complex plane $\mathbb{C}$ that satisfies an $A_p$-type condition. As applications, we establish some results on the $r$-summability of differentiation and integration operators, Volterra-type operators and composition operators. Especially, we completely characterize the boundedness of Volterra-type operators and composition operators on vector-valued Fock spaces for all $1<p<\infty$, which were left open before for the case $1<p<2$. |
| title | Absolutely summing Carleson embeddings on weighted Fock spaces with $A_{\infty}$-type weights |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2505.16109 |