HOLOMORPHIC EXTENSION OF CR-FUNCTIONS WITH SINGULARITIES ON A GENERIC MANIFOLD

Let GAMMA be a smooth generic manifold with nonzero Levi form in a domain of holomorphy OMEGA subset-of C(n) with n > 1 . Let OMEGA(GAMMA) subset-of OMEGA be the domain adjacent to GAMMA to which all CR-functions defined on GAMMA extend holomorphically. Let K = k(OMEGA) subset-of OMEGA be a holomorphically convex compact set. We show that every CR-function on GAMMA\K of class L(loc)1(GAMMA\K) extends holomorphically to OMEGA(GAMMA)\K. When n = 2 the manifold GAMMA must be closed, i.e., partial derivative GAMMA = 0. As a corollary we deduce a result on the removal of singularities of CR-functions of finite order of growth near K. The proof uses the integral representation of Airapetyan and Khenkin.