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

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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
DOIs
StatePublished - Nov 2001
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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