On Gaussian Nikolskii-Besov classes
The authors summarize the contents of this paper in the abstract of the paper as follows: In this note we study Nikolskii-Besov classes of functions of fractional smoothness on finite-dimensional and infinite-dimensional spaces with Gaussian measures. We prove the equivalence of two characterizations of these classes: one is based on a certain nonlinear integration by parts formula and the other one is given in terms of the Ornstein-Uhlenbeck semigroup. In addition, we obtain a new Poincaré-type inequality. The case of Lebesgue measure has been considered in [Dokl. Math. 96, No. 2, 449--453 (2017; Zbl 1448.46025)] (see also [\textit{V. I. Bogachev} et al., Dokl. Math. 94, No. 1, 453--457 (2016; Zbl 1352.60054)]).
scientific article; zbMATH DE number 6828257