\(L^p\) and \(H^p\) extensions of holomorphic functions from subvarieties of analytic polyhedra
type: Item
instance of: scholarly article
title: \(L^p\) and \(H^p\) extensions of holomorphic functions from subvarieties of analytic polyhedra
zbMATH Open document ID: 0934.32002
author: Kenzō Adachi
author: Mats Andersson
author: Hong Rae Cho
published in: Pacific Journal of Mathematics
publication date: 2000-04-29T00:00:00Z
review text: Let \(V\) be a regular subvariety of a non-degenerate analytic polyhedron \(\Omega\subset\mathbb{C}^n\). If \(V\) intersects \(\partial\Omega\) transversally in a certain sense, then each bounded holomorphic function on \(V\) has a bounded holomorphic extension to \(\Omega\). Furthermore, a function in \(H^p(V)\) has an extension in \(H^p(\Omega)\). Under a weaker transversality condition each \(f\in{\mathcal O}(V)\cap L^p(V)\) has an extension to a function on \({\mathcal O}(\Omega)\cap L^p(\Omega)\), \(p<\infty\).
reviewed by: Hong Rae Cho
Mathematics Subject Classification ID: 32A25
Mathematics Subject Classification ID: 32D15
zbMATH DE Number: 1356075
zbMATH Keywords: \(L^p\) and \(H^p\) extensions of holomorphic functions
zbMATH Keywords: subvariety
zbMATH Keywords: analytic polyhedron
zbMATH Keywords: transversality condition
MaRDI profile type: Publication
full work available at URL: pjm.1999.189.201
OpenAlex ID: W2003386349
DOI: 10.2140/PJM.1999.189.201
description: scientific article; zbMATH DE number 1356075