Hardy Number of Koenigs Domains: Sharp Estimate

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 $f:\mathbb{D}\to \Omega$ belongs to the Hardy space $H^p(\mathbb{D})$ for all $p<1/2$.

This draft is not for submission. It has been incorporated as an improvement in a previous work, see arXiv:2312.17101