On Gaussian Nikolskii-Besov classes
type: Item
instance of: scholarly article
title: On Gaussian Nikolskii-Besov classes
zbMATH Open document ID: 1381.28013
DOI: 10.1134/S1064562417050295
author: Svetlana N. Popova
author: Vladimir I. Bogachev
author: Egor D. Kosov
published in: Doklady Mathematics
publication date: 2018-01-22T00:00:00Z
review text: 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)]).
reviewed by: Kun Soo Chang
Mathematics Subject Classification ID: 28C20
zbMATH DE Number: 6828257
zbMATH Keywords: Gaussian Nikolskii-Besov classes
zbMATH Keywords: fractional smoothness
zbMATH Keywords: nonlinear integration by parts formula
zbMATH Keywords: Ornstein-Uhlenbeck semigroup
zbMATH Keywords: Poincaré-type inequality
MaRDI profile type: Publication
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full work available at URL: s1064562417050295
OpenAlex ID: W2766143811
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description: scientific article; zbMATH DE number 6828257