Email this article On Gaussian Nikolskii–Besov classes
- Authors: Bogachev V.I.1,2,3, Kosov E.D.1, Popova S.N.1
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Affiliations:
- Department of Mechanics and Mathematics
- National Research University Higher School of Economics
- St. Tikhon’s Orthodox Humanitarian University
- Issue: Vol 96, No 2 (2017)
- Pages: 498-502
- Section: Mathematics
- URL: https://journal-vniispk.ru/1064-5624/article/view/225399
- DOI: https://doi.org/10.1134/S1064562417050295
- ID: 225399
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Abstract
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]).
About the authors
V. I. Bogachev
Department of Mechanics and Mathematics; National Research University Higher School of Economics; St. Tikhon’s Orthodox Humanitarian University
Author for correspondence.
Email: vibogach@mail.ru
Russian Federation, Moscow; Moscow; Moscow
E. D. Kosov
Department of Mechanics and Mathematics
Email: vibogach@mail.ru
Russian Federation, Moscow
S. N. Popova
Department of Mechanics and Mathematics
Email: vibogach@mail.ru
Russian Federation, Moscow
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