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Mat. Sb., 2019, Volume 210, Number 5, Pages 41–71 (Mi msb9058)  

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.

Funding Agency Grant Number
Russian Science Foundation 17-11-01058
This research was supported by the Russian Science Foundation under grant no. 17-11-01058.


DOI: https://doi.org/10.4213/sm9058

Full text: PDF file (690 kB)
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English version:
Sbornik: Mathematics, 2019, 210:5, 663–692

Bibliographic databases:

UDC: 517.518.2
MSC: Primary 46E35; Secondary 28C20, 46G12
Received: 31.12.2017 and 24.04.2018

Citation: E. D. Kosov, “Besov classes on finite and infinite dimensional spaces”, Mat. Sb., 210:5 (2019), 41–71; Sb. Math., 210:5 (2019), 663–692

Citation in format AMSBIB
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