H²-Corona problem on δ-regular domains

2022/06/09 by Bo-Yong Chen, Chen, Bo-Yong, Xu Xing +1
Computer Science · Mathematics · #32A10 #32A35 #32T25 #Advanced Mathematical Modeling in Engineering #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2206.04455

openalex publication_date 2022/06/09 · openalex created_date 2022/06/13 · openalex updated_date 2026/07/28

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.

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