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arXiv · 2206.04455

$H^2-$Corona problem on $\delta-$regular domains

Bo-Yong Chen·Xu Xing
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Abstract

We prove an $H^2-$Corona theorem with estimate $C(\delta)=C\delta^{-1-q}|\log \delta|$ for $\delta\ll 1$ on delta-regular domains, where $q=\min\{n,m-1\}$ and $m$ is the number of generators. This class of domains includes smooth bounded domains with defining functions that are plurisubharmonic on boundaries and pseudoconvex domains of D'Angelo finite type.

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Bo-Yong Chen, Xu Xing. 2022-06-09. $H^2-$Corona problem on $\delta-$regular domains. https://arxiv.org/abs/2206.04455

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