CR extension for \(L^ p\) CR functions on a quadric submanifold of \(\mathbb C^ n\).
type: Item
instance of: scholarly article
title: CR extension for \(L^ p\) CR functions on a quadric submanifold of \(\mathbb C^ n\).
zbMATH Open document ID: 1090.32020
author: Albert Boggess
published in: Pacific Journal of Mathematics
publication date: 2002-10-22T00:00:00Z
review text: Let \(M\) be the CR submanifold of \(C^m_w\times C^d_z\) defined by equations \(\Re z_i=q_i(w,\bar w),\; i=1,...,d\), with \(q_i\) a Hermitian symmetric form in \(C^m_w\). Denote by CR\(^p(M)\) the space of \(L^p\) CR functions on \(M\). The author shows that functions of CR\(^p(M)\) extend to \(H^p\) function on the interior of the convex hull of \(M\). This result is a global version of the one obtained with \textit{A. Nagel} [Pac. J. Math. 167, No. 1, 1--47 (1995; Zbl 0848.32015)]. As part of the proof, he establishes a semi-global version of the approximation theorem of \textit{M. S. Baouendi} and \textit{F. Treves} [Ann. Math. (2) 113, No. 2, 387--421; (1981; Zbl 0491.35036)] for submanifolds which are graphs of functions with polynomial growth.
reviewed by: Mauro Nacinovich
Mathematics Subject Classification ID: 32V25
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 1818912
zbMATH Keywords: quadric submanifolds
zbMATH Keywords: CR functions
MaRDI profile type: Publication
full work available at URL: pjm.2001.201.1
OpenAlex ID: W2032015802
DOI: 10.2140/PJM.2001.201.1
description: scientific article; zbMATH DE number 1818912