Holomorphic approximation on compact pseudoconvex complex manifolds

Abstract

Let\(\overline M \) 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)∩ Hm(M), where Hm(M) is the Sobolev space of order m. Then f can be approximated by holomorphic functions on\(\overline M \) in the Sobolev space Hm(M). Also, we get a holomorphic approximation theorem near a boundary point of finite type.