Hardy Number of Koenigs Domains: Sharp Estimate
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909222938083328 |
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| author | Contreras, Manuel D. Cruz-Zamorano, Francisco J. Kourou, Maria Rodríguez-Piazza, Luis |
| author_facet | Contreras, Manuel D. Cruz-Zamorano, Francisco J. Kourou, Maria Rodríguez-Piazza, Luis |
| contents | Let $Ω$ be a regular Koenigs domain in the complex plane $\mathbb{C}$. We prove that the Hardy number of $Ω$ is greater or equal to $1/2$. That is, every holomorphic function in the unit disc $f \colon \mathbb{D} \to Ω$ belongs to the Hardy space $H^{p}(\mathbb{D})$ for all $p<1/2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_17621 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hardy Number of Koenigs Domains: Sharp Estimate Contreras, Manuel D. Cruz-Zamorano, Francisco J. Kourou, Maria Rodríguez-Piazza, Luis Complex Variables Primary 30D05, 30H10, 30C85, Secondary 39B32, 37F99 Let $Ω$ be a regular Koenigs domain in the complex plane $\mathbb{C}$. We prove that the Hardy number of $Ω$ is greater or equal to $1/2$. That is, every holomorphic function in the unit disc $f \colon \mathbb{D} \to Ω$ belongs to the Hardy space $H^{p}(\mathbb{D})$ for all $p<1/2$. |
| title | Hardy Number of Koenigs Domains: Sharp Estimate |
| topic | Complex Variables Primary 30D05, 30H10, 30C85, Secondary 39B32, 37F99 |
| url | https://arxiv.org/abs/2405.17621 |