The Boggess-Polking extension theorem for CR functions on manifolds with corners

We give the "boundary version" of the Boggess-Polking CR extension theorem. Let M and N be real generic submanifolds of C-n with Nsubset ofM and let V be a "wedge" in M with "edge" N and "profile" Sigmasubset ofT(N)M in a neighborhood of a point z(o). We identify in natural manner [GRAPHICS] and assume that for a holomorphic vector field L tangent to M and verifying L(z(o)) + (L) over bar (z(o)) is an element of k(Sigma(z o)) we have that the Levi form jL(L)z(o) := j ((1)/(2i) [L (L) over bar ]z(o)) takes a value iv(o) is an element of TMXz o, iv(o) not equal 0 (say \v(o)\ = 1). Then we prove that CR functions on V extend For All(epsilon) to a wedge V-1 "attached" to V in direction of a vector field iV such that \pr(iV(z(o)))-iv(o) \<ε (where pr is the projection pr: TNX→TMX|N). We then prove that when the Levi cone "relative to Σ" iZ(Σ) = convex hull {jL(L)(z o)|L(z(o))+<(L)over bar>z(o)) is an element of k(Sigma()z o)} is open in TMX, then CR functions extend to a "full" wedge with edge N (that is, with a profile which is an open cone of TNX). Finally, we prove that if f is defined in a couple of wedges +/-V with profiles +/-Sigma such that iZ(Sigma) = TMX, and is continuous up to N, then f is in fact holomorphic at z(o).