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arXiv · 2405.17621

Hardy Number of Koenigs Domains: Sharp Estimate

Manuel D. Contreras·Francisco J. Cruz-Zamorano·Maria Kourou·Luis Rodríguez-Piazza
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Abstract

Let $\Omega$ be a regular Koenigs domain in the complex plane $\mathbb{C}$. We prove that the Hardy number of $\Omega$ is greater or equal to $1/2$. That is, every holomorphic function in the unit disc $f \colon \mathbb{D} \to \Omega$ belongs to the Hardy space $H^{p}(\mathbb{D})$ for all $p<1/2$.

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Manuel D. Contreras, Francisco J. Cruz-Zamorano, Maria Kourou, Luis Rodríguez-Piazza. 2024-05-27. Hardy Number of Koenigs Domains: Sharp Estimate. https://arxiv.org/abs/2405.17621

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