Pseudoconvex Domains in Almost Complex Abstract Wiener Spaces

The ∂-operator on an almost complex abstract Wiener space (B, H, μ, J) is defined by making use of the Malliavin calculus. The authors then study pseudoconvex domains in B, domains where the ∂-equations ∂u = ƒ are solvable. As an application, they establish an approximation theorem of holomorphic forms and a Dolbeault type theorem. Examples of such domains, obtained through SDE, one also discussed.