Anticipating flows on the Wiener space generated by vector fields of low regularity

Sobolev spaces for Banach space valued Wiener functionals are constructed using the operator norm for the H-derivatives. The corresponding Sobolev norms are shown to be strictly weaker than the usual Malliavin Sobolev norms. Existing results on flows on an abstract Wiener space generated by a vector field are generalized to the case where the Vector field is a sum of a not necessarily bounded skew-adjoint operator and a non-linear part whose regularity is measured by the new Sobolev norms. This is equivalent to a non-linear perturbation of a semi-group Of rotations. (C) 1996 Academic Press, Inc.