On flows associated to Sobolev vector fields in Wiener spaces: An approach à la DiPerna–Lions

In this paper we extend the DiPerna–Lions theory of flows associated to Sobolev vector fields to the case of Cameron–Martin-valued vector fields in Wiener spaces E having a Sobolev regularity. The proof is based on the analysis of the continuity equation in E, and on uniform (Gaussian) commutator estimates in finite-dimensional spaces.