Extension of CR-forms and related problems
type: Item
instance of: scholarly article
title: Extension of CR-forms and related problems
zbMATH Open document ID: 0625.32013
author: Alessandro Perotti
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1987-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108069
review text: Let D be a bounded domain of \({\mathbb{C}}^ n\), \(n\geq 3\) and let \(\partial D=S\cup A\) when S is a real \(C^ 1\) hypersurface with boundary \(\partial S\) and A is a non empty piecewise \(C^ 1\) real hypersurface. Assume there exists a family \(\{V_ j\}_{j\in {\mathbb{N}}}\) of (n-3)-complete open subsets such that \(\bar V{}_{j+1}\subset V_ j\) and \((\cup_{j}V_ j)\cap \bar D=\bar A\) (and this is always true if A is contained in the zero-set of a pluriharmonic function). Then the following is proved: Every Lipschitz CR-form of type (p,0) on \(\overset\circ S\) can be extended on D by a (p,0)-form holomorphic on D and continuous on \(D\cup\overset\circ S\). For CR-forms of type (p,q) the author proves a jump theorem: assume that \(V_ j\) is (n-s-2)-complete; then every regular CR-form of type (p,q) where \(0\leq p\leq n\), \(0\leq q\leq s-1\) is the jump across S of two \(\partial\)-closed forms on D and \({\mathbb{C}}^ n\setminus (\bar D\cup (\cap_{j}\bar V_ j))\), respectively. When S is assumed to be strictly pseudoconvex, as an application of this result, the author obtains an extension theorem for CR-forms of type (p,q).
Mathematics Subject Classification ID: 32D99
Mathematics Subject Classification ID: 32V40
Mathematics Subject Classification ID: 32F10
zbMATH DE Number: 4015145
zbMATH Keywords: extension of CR forms
reviewed by: Giuseppe Tomassini
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4015145