An extension of H. Cartan's theorem

In this article we prove that if D subset of C-n, n greater than or equal t o 2, is a bounded pseudoconvex domain with real analytic boundary, then for each g(z) is an element of Aut(D), there exists a fixed open neighborhood Omega(g) of (D) over bar and an open neighborhood V-g of g(z) in Aut(D) suc h that any h(z) is an element of V-g can be extended holomorphically to Ome ga(g), and that the action defined by pi:V-g X Omega(g) --> C-n (f, z) bar right arrow pi(f, z) = f(z) is real analytic in joint variables. This extends H. Cartan's theorem beyon d the boundary. Some applications are also discussed here.