Analyticity of Nonsymmetric Ornstein-Uhlenbeck Semigroup with Respect to a Weighted Gaussian Measure

In this paper we show that the realization in L p(X, ν∞) of a nonsymmetric Ornstein-Uhlenbeck operator Lp is sectorial for any p∈ (1 , + ∞) and we provide an explicit sector of analyticity. Here, (X, μ∞, H∞) is an abstract Wiener space, i.e., X is a separable Banach space, μ∞ is a centred nondegenerate Gaussian measure on X and H∞ is the associated Cameron-Martin space. Further, ν∞ is a weighted Gaussian measure, that is, ν∞= e−Uμ∞ where U is a convex function which satisfies some minimal conditions. Our results strongly rely on the theory of nonsymmetric Dirichlet forms and on the divergence form of the realization of L2 in L 2(X, ν∞).