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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.17101 |
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| _version_ | 1866909223455031296 |
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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 | This work studies the Hardy number for the class of hyperbolic planar domains satisfying Abel's inclusion property, which are usually known as Koenigs domains. More explicitly, we prove that for all regular domains in the above class, the Hardy number is greater or equal than $1/2$, and this lower bound is sharp. In contrast to this result, we provide examples of general domains whose Hardy numbers are arbitrarily small. Additionally, we outline the connection of the aforementioned class of domains with the discrete dynamics of the unit disc and obtain results on the range of Hardy number of Koenigs maps, in the hyperbolic and parabolic case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17101 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Hardy number of Koenigs domains Contreras, Manuel D. Cruz-Zamorano, Francisco J. Kourou, Maria Rodríguez-Piazza, Luis Complex Variables Primary 30D05, 30H10, 30C85, Secondary 39B32, 37F99 This work studies the Hardy number for the class of hyperbolic planar domains satisfying Abel's inclusion property, which are usually known as Koenigs domains. More explicitly, we prove that for all regular domains in the above class, the Hardy number is greater or equal than $1/2$, and this lower bound is sharp. In contrast to this result, we provide examples of general domains whose Hardy numbers are arbitrarily small. Additionally, we outline the connection of the aforementioned class of domains with the discrete dynamics of the unit disc and obtain results on the range of Hardy number of Koenigs maps, in the hyperbolic and parabolic case. |
| title | On the Hardy number of Koenigs domains |
| topic | Complex Variables Primary 30D05, 30H10, 30C85, Secondary 39B32, 37F99 |
| url | https://arxiv.org/abs/2312.17101 |