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.

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