To be more specific: Let $Q\subset\mathbb{C}$ be a Lipschitz bounded domain, and $V$ is a compact complex manifold without boundary. Consider the set of holomorphic maps $f:Q\rightarrow V$, and $f\in H^s(Q,V)$, with $s$ sufficiently large(say $s>3$). The notation $H^s(Q,V)$ means the derivatives up to order $s$ are in $L^2$(under local coordinates of $V$) Now the question is whether this set forms a complex Hilbert manifold? How do we define the coordinate chart?

Actually all I need is to identify the neighborhood of some give holomorphic map $f_0$ with an open subset of a Hilbert space(without asking for smoothness of coordinate transformation)