On Gaussian Nikolskii–Besov classes

In this note we study Nikolskii–Besov classes of functions of fractional smoothness on finitedimensional 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 th...

Full description

Saved in:
Bibliographic Details
Published in:Doklady. Mathematics 2017-09, Vol.96 (2), p.498-502
Main Authors: Bogachev, V. I., Kosov, E. D., Popova, S. N.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Smoothness
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this note we study Nikolskii–Besov classes of functions of fractional smoothness on finitedimensional 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 [1] (see also [2, 3]).
ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562417050295