CR extension for Lp CR functions on a quadric submanifold of Cn

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3 Citations (Scopus)

Abstract

We consider the space, CRp(M), consisting of CR functions which also lie in Lp(M) on a quadric submanifold M of Cn of codimension at least one. For 1 ≤ p ≤ ∞, we prove that each element in CRp(M) extends uniquely to an Hp function on the interior of the convex hull of M. As part of the proof, we establish a semi-global version of the CR approximation theorem of Baouendi and Treves for submanifolds which are graphs and whose graphing functions have polynomial growth.

Original languageEnglish (US)
Pages (from-to)1-18
Number of pages18
JournalPacific Journal of Mathematics
Volume201
Issue number1
StatePublished - Nov 2001
Externally publishedYes

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CR Functions
Quadric
Submanifolds
Polynomial Growth
Approximation Theorem
Convex Hull
Codimension
Interior
Graph in graph theory

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

CR extension for Lp CR functions on a quadric submanifold of Cn . / Boggess, Albert.

In: Pacific Journal of Mathematics, Vol. 201, No. 1, 11.2001, p. 1-18.

Research output: Contribution to journalArticle

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