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

This article is cited in 3 scientific papers (total in 3 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.

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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  • https://doi.org/10.4213/sm9058
  • http://mi.mathnet.ru/eng/msb/v210/i5/p41

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kosov E.D., “On Fractional Regularity of Distributions of Functions in Gaussian Random Variables”, Fract. Calc. Appl. Anal., 22:5 (2019), 1249–1268  crossref  mathscinet  isi
    2. Vladimir I. Bogachev, Egor D. Kosov, Svetlana N. Popova, “A new approach to Nikolskii–Besov classes”, Mosc. Math. J., 19:4 (2019), 619–654  mathnet  crossref
    3. G. I. Zelenov, “Drobnaya gladkost raspredelenii trigonometricheskikh polinomov na prostranstve s gaussovskoi meroi”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 31 (2020), 78–95  mathnet  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
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