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Moscow Mathematical Journal, 2019, Volume 19, Number 4, Pages 619–654
DOI: https://doi.org/10.17323/1609-4514-2019-19-4-619-654 (Mi mmj748) 		 
This article is cited in 9 scientific papers (total in 9 papers)

A new approach to Nikolskii–Besov classes

Vladimir I. Bogachevab, Egor D. Kosovab, Svetlana N. Popovac

a Department of Mechanics and Mathematics, Moscow State University, 119991 Moscow, Russia
b National Research University Higher School of Economics, Myasnitskaya 20, 101000 Moscow, Russia
c Department of Innovation and High Technology, Moscow Institute of Physics and Technology (State University), 9 Institutskiy per., 141700 Dolgoprudny, Moscow Region, Russia
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DOI: https://doi.org/10.17323/1609-4514-2019-19-4-619-654
Abstract: We give a new characterization of Nikolskii–Besov classes of functions of fractional smoothness by means of a nonlinear integration by parts formula in the form of a nonlinear integral inequality. A similar characterization is obtained for Nikolskii–Besov classes with respect to Gaussian measures on finite- and infinite-dimensional spaces.
Key words and phrases: Nikolskii–Besov class, integration by parts formula, fractional Sobolev class, Ornstein–Uhlenbeck semigroup.
Funding agency Grant number
Russian Science Foundation 17-11-01058
This research was supported by the Russian Science Foundation Grant 17-11-01058 at Lomonosov Moscow State University.
Bibliographic databases:
Document Type: Article
MSC: Primary 46E35; Secondary 28C20, 46G12
Language: English
Citation: Vladimir I. Bogachev, Egor D. Kosov, Svetlana N. Popova, “A new approach to Nikolskii–Besov classes”, Mosc. Math. J., 19:4 (2019), 619–654
Citation in format AMSBIB
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\paper A new approach to Nikolskii--Besov classes
\jour Mosc. Math.~J.
\yr 2019
\vol 19
\issue 4
\pages 619--654
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