Invariant metric estimates for \(\overline\partial\) on some pseudoconvex domains
type: Item
instance of: scholarly article
title: Invariant metric estimates for \(\overline\partial\) on some pseudoconvex domains
zbMATH Open document ID: 1038.32004
DOI: 10.1007/BF02388794
published in: Arkiv för Matematik
publication date: 2004-03-15T00:00:00Z
review text: Let \(\Omega\subset {\mathbb C}^n\) be a smoothly bounded pseudo-convex domain of finite type. The main theorem of the paper under review asserts that, if \(n=2\), or if \(\Omega\) satisfies the further assumption of being strongly pseudo-convex, convex, or decoupled, then there exists a constant \(C\) such that, if \(\alpha\) is a \(\overline{\partial}\)-closed \((n,1)\)-form on \(\Omega\), then there exists an \((n,0)\)-form \(u\) solving the equation \(\overline{\partial}u=\alpha\), and which satisfies the estimate \[ \| u\| _I\leq C\| \alpha\| _I, \] where \(\| \;\| _I\) is the norm associated to any of the Carathéodory, Bergman or Kobayashi metrics on \(\Omega\).
reviewed by: Line Baribeau
Mathematics Subject Classification ID: 32A25
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 32T99
Mathematics Subject Classification ID: 32F45
zbMATH DE Number: 2057379
zbMATH Keywords: pseudo-convex domain of finite type
author: J. D. McNeal
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02388794
OpenAlex ID: W1989431940
description: scientific article; zbMATH DE number 2057379