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

TL;DR

This paper establishes an $H^2$-Corona theorem with explicit estimates on a broad class of $ ext{delta}$-regular domains, including smooth and pseudoconvex domains of finite type, advancing the understanding of function theory in complex analysis.

Contribution

It proves an $H^2$-Corona theorem with explicit bounds on $ ext{delta}$-regular domains, encompassing smooth and pseudoconvex domains of finite type, with novel estimates.

Findings

Established an $H^2$-Corona theorem with explicit estimate $C( ext{delta})$

Included classes of domains such as smooth bounded and pseudoconvex of finite type

Provided bounds depending on $ ext{delta}$ and domain parameters

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.