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JOURNALS // Matematicheskii Sbornik // Archive
Mat. Sb., 2019 Volume 210, Number 5, Pages 41–71 (Mi sm9058)
This article is cited in 13 papers

Besov classes on finite and infinite dimensional spaces

E. D. Kosov

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: We give an equivalent description of Besov spaces in terms of a new modulus of continuity. Then we use a similar approach to introduce Besov classes on an infinite-dimensional space endowed with a Gaussian measure.
Bibliography: 25 titles.

Keywords: Besov space, embedding theorem, Gaussian measure, Ornstein-Uhlenbeck semigroup.

UDC: 517.518.2

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

Received: 31.12.2017 and 24.04.2018

DOI: 10.4213/sm9058


 English version: Sbornik: Mathematics, 2019, 210:5, 663–692

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© Steklov Math. Inst. of RAS, 2026