Manifolds Of Holomorphic Mappings From Strongly Pseudoconvex Domains

Let D be a bounded strongly pseudoconvex domain in a Stein manifold, and let Y be a complex manifold. We show that many classical spaces of maps (D) over bar -> Y which are holomorphic in D are infinite dimensional complex manifolds which are modeled on locally convex topological vector spaces (Banach, Hilbert or Frechet). This holds in particular for Holder and Sobolev spaces of holomorphic maps.