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

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.

Several mistakes are corrected; Lemma 4.2 is added to explain the density