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Sbornik: Mathematics, 2019, Volume 210, Issue 5, Pages 663–692
DOI: https://doi.org/10.1070/SM9058 (Mi sm9058) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Besov classes on finite and infinite dimensional spaces

E. D. Kosov

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
English version PDF (557 kB) Citations (12) Russian version article
References:
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DOI: https://doi.org/10.1070/SM9058
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.
Received: 31.12.2017 and 24.04.2018
Bibliographic databases:
Document Type: Article
UDC: 517.518.2
MSC: Primary 46E35; Secondary 28C20, 46G12
Language: English
Original paper language: Russian
Citation: E. D. Kosov, “Besov classes on finite and infinite dimensional spaces”, Sb. Math., 210:5 (2019), 663–692
Citation in format AMSBIB
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\by E.~D.~Kosov
\paper Besov classes on finite and infinite dimensional spaces
\jour Sb. Math.
\yr 2019
\vol 210
\issue 5
\pages 663--692
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Linking options:
  • https://www.mathnet.ru/eng/sm9058
  • https://doi.org/10.1070/SM9058
  • https://www.mathnet.ru/eng/sm/v210/i5/p41
    • This publication is cited in the following 12 articles:
    1. Egor Kosov, Anastasia Zhukova, “Improved bounds for the total variation distance between stochastic polynomials”, Stoch. Proc. Appl., 170 (2024), 104279–15  mathnet  crossref  mathscinet  isi
    2. Oscar Domínguez, Yinqin Li, Sergey Tikhonov, Dachun Yang, Wen Yuan, “A unified approach to self-improving property via K-functionals”, Calc. Var., 63:9 (2024)  crossref
    3. V. I. Bogachev, “Sobolev and Besov Classes on Infinite-Dimensional Spaces”, Proc. Steklov Inst. Math., 323 (2023), 59–80  mathnet  crossref  crossref  mathscinet
    4. E. D. Kosov, “Regularity of Distributions of Sobolev Mappings in Abstract Settings”, Math. Notes, 114:5 (2023), 862–874  mathnet  mathnet  crossref  mathscinet  scopus
    5. E. D. Kosov, “Distributions of Polynomials in Gaussian Random Variables under Constraints on the Powers of Variables”, Funct. Anal. Appl., 56:2 (2022), 101–109  mathnet  crossref  crossref
    6. E. D. Kosov, “Regularity of linear and polynomial images of Skorohod differentiable measures”, Advances in Mathematics, 397 (2022), 108193  crossref  mathscinet
    7. G. I. Zelenov, “On distributions of trigonometric polynomials in Gaussian random variables”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 37 (2021), 77–92  mathnet  crossref
    8. V. I. Bogachev, “Chebyshev–Hermite polynomials and distributions of polynomials in Gaussian random variables”, Theory Probab. Appl., 66:4 (2022), 550–569  mathnet  crossref  crossref  zmath
    9. V. I. Bogachev, “On Skorokhod differentiable measures”, Ukr. Mat. Zhurn., 72:9 (2020), 1159  crossref  crossref  mathscinet  isi  scopus
    10. 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
    11. E. D. Kosov, “On fractional regularity of distributions of functions in gaussian random variables”, Fract. Calc. Appl. Anal., 22:5 (2019), 1249–1268  crossref  mathscinet  isi
    12. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:81
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