The H2-Corona problem on delta-regular domains

Abstract

We prove an H2-Corona theorem with estimate C(δ)=Cδ−1−q|log⁡δ| for δ≪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.