Vladimir I. Bogachev, Egor D. Kosov, Svetlana N. Popova, “A new approach to Nikolskii–Besov classes”, Mosc. Math. J., 2019, Volume 19, Number 4,Pages <nobr>619

This article is cited in 9 papers

A new approach to Nikolskii–Besov classes

Vladimir I. Bogachev^ab, Egor D. Kosov^ab, Svetlana N. Popova^c

^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

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.

MSC: Primary 46E35; Secondary 28C20, 46G12

Language: English

DOI: 10.17323/1609-4514-2019-19-4-619-654