Holomorphic approximation on compact pseudoconvex complex manifolds

Abstract

Abstract. Let M be a smoothly bounded compact pseudoconvex complex manifold of finite type in the sense of D'Angelo such that the complex structure of M extends smoothly up to bM . Let m be an arbitrary nonnegative integer. Let f be a function in H(M ) ∩ H m (M ), where H m (M ) is the Sobolev space of order m. Then f can be approximated by holomorphic functions on M in the Sobolev space H m (M ). Also, we get a holomorphic approximation theorem near a boundary point of finite type.