Hölder and \(L^ p\) estimates for \({\bar \partial}_ b\) on weakly pseudo-convex boundaries in \({\mathbb C}^ 2\)
type: Item
instance of: scholarly article
title: Hölder and \(L^ p\) estimates for \({\bar \partial}_ b\) on weakly pseudo-convex boundaries in \({\mathbb C}^ 2\)
zbMATH Open document ID: 0617.32031
DOI: 10.1007/BF01458533
published in: Mathematische Annalen
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164344
review text: Let M be the boundary of a weakly pseudoconvex domain of strict finite type in \({\mathbb{C}}^ 2\). We solve the tangential Cauchy-Riemann equation \({\bar \partial}_ b\) on M globally with sharp Hölder and \(L^ p\) estimates for the solutions. The regularity of the solutions reflects the finite type condition, and examples are given to show that these estimates are sharp in the Hölder and \(L^ p\) classes. This result shows that \({\bar \partial}_ b\) has closed range on M globally, even though locally \({\bar \partial}_ b\) may not have closed range in any function space.
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 32T99
zbMATH DE Number: 4000372
zbMATH Keywords: pseudoconvex domain
zbMATH Keywords: tangential Cauchy-Riemann equation
zbMATH Keywords: Hölder and \(L^ p\) estimates
author: Mei-Chi Shaw
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4000372