CR extension for L^p CR functions on a quadric submanifold of Cⁿ

Albert Boggess

Vol. 201 (2001), No. 1, 1–18

DOI: 10.2140/pjm.2001.201.1

Abstract

We consider the space, CR^p(M), consisting of CR functions which also lie in L^p(M) on a quadric submanifold M of Cⁿ of codimension at least one. For 1 ≤ p ≤∞, we prove that each element in CR^p(M) extends uniquely to an H^p 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.

Milestones

Received: 16 November 1999

Revised: 18 July 2000

Published: 1 November 2001