On Gaussian Nikolskii–Besov classes


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Аннотация

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]).

Авторлар туралы

V. Bogachev

Department of Mechanics and Mathematics; National Research University Higher School of Economics; St. Tikhon’s Orthodox Humanitarian University

Хат алмасуға жауапты Автор.
Email: vibogach@mail.ru
Ресей, Moscow; Moscow; Moscow

E. Kosov

Department of Mechanics and Mathematics

Email: vibogach@mail.ru
Ресей, Moscow

S. Popova

Department of Mechanics and Mathematics

Email: vibogach@mail.ru
Ресей, Moscow

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