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Moscow Mathematical Journal

Volume 19, Issue 4, October–December 2019  pp. 619–654.

A New Approach to Nikolskii–Besov Classes

Authors:  Vladimir I. Bogachev (1), Egor D. Kosov (1), and Svetlana N. Popova (2)
Author institution:(1) Department of Mechanics and Mathematics, Moscow State University, 119991 Moscow, Russia
National Research University Higher School of Economics, Myasnitskaya 20, 101000 Moscow, Russia
(2) Department of Innovation and High Technology, Moscow Institute of Physics and Technology (State University), 9 Institutskiy per., 141700 Dolgoprudny, Moscow Region, Russia


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.

2010 Math. Subj. Class. Primary: 46E35; Secondary: 28C20, 46G12.

Keywords: Nikolskii–Besov class, integration by parts formula, fractional Sobolev class, Ornstein–Uhlenbeck semigroup.

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