CR extension for L-p CR functions on a quadric submanifold of C-n

We consider the space, CRp (M), consisting of CR functions which also lie i n L-p (M) on a quadric submanifold M of C-n of codimension at least one. Fo r 1 less than or equal to p less than or equal to infinity, we prove that e ach element in CRp (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 v ersion of the CR approximation theorem of Baouendi and Treves for submanifo lds which are graphs and whose graphing functions have polynomial growth.