Sobolev spaces with respect to a weighted Gaussian measure in infinite dimensions

Let X be a separable Banach space endowed with a nondegenerate centered Gaussian measure μ and let w be a positive function on X such that w W1,s(X,μ) and log w ∈W1,t(X,μ) for some s > 1 and t > s′. In this paper, we introduce and study Sobolev spaces with respect to the weighted Gaussian measure ν:= wμ. We obtain results regarding the divergence operator (i.e. the adjoint in L2 of the gradient operator along the Cameron-Martin space) and the trace of Sobolev functions on hypersurfaces x ∈X|G(x) = 0, where G is a suitable version of a Sobolev function.