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

Abstract

Let [Formula: see text] be a separable Banach space endowed with a nondegenerate centered Gaussian measure [Formula: see text] and let [Formula: see text] be a positive function on [Formula: see text] such that [Formula: see text] and [Formula: see text] for some [Formula: see text] and [Formula: see text]. In this paper, we introduce and study Sobolev spaces with respect to the weighted Gaussian measure [Formula: see text]. We obtain results regarding the divergence operator (i.e. the adjoint in [Formula: see text] of the gradient operator along the Cameron–Martin space) and the trace of Sobolev functions on hypersurfaces [Formula: see text], where [Formula: see text] is a suitable version of a Sobolev function.