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Uspekhi Mat. Nauk, 2016, Volume 71, Issue 4(430), Pages 107–154 (Mi umn9721)  

This article is cited in 10 scientific papers (total in 10 papers)

Distributions of polynomials on multidimensional and infinite-dimensional spaces with measures

V. I. Bogachev

National Research University "Higher School of Economics"

Abstract: This paper provides a survey of recent investigations connected with distributions of polynomials on multi- and infinite-dimensional spaces with measures. The most important results on estimates (independent of the number of variables) for distribution functions and integral norms and also on convergence of the distributions of polynomials in variation and in the Kantorovich metric are presented. Interesting open problems in this area at the junction of the theory of functions, probability theory, and measure theory are discussed.
Bibliography: 131 titles.

Keywords: polynomials, distribution function, measurable polynomials, Gaussian measure, convex measure, logarithmically concave measure, convergence in variation, Kantorovich metric.

Funding Agency Grant Number
Russian Science Foundation 14-11-00196
This research was supported by grant no. 14-11-00196 from the Russian Science Foundation (at~Moscow State University).


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English version:
Russian Mathematical Surveys, 2016, 71:4, 703–749

Bibliographic databases:

UDC: 519.2
MSC: Primary 28C20, 46G12, 46G25; Secondary 60B10, 60B11, 60E05
Received: 09.05.2016

Citation: V. I. Bogachev, “Distributions of polynomials on multidimensional and infinite-dimensional spaces with measures”, Uspekhi Mat. Nauk, 71:4(430) (2016), 107–154; Russian Math. Surveys, 71:4 (2016), 703–749

Citation in format AMSBIB
\by V.~I.~Bogachev
\paper Distributions of polynomials on multidimensional and infinite-dimensional spaces with measures
\jour Uspekhi Mat. Nauk
\yr 2016
\vol 71
\issue 4(430)
\pages 107--154
\jour Russian Math. Surveys
\yr 2016
\vol 71
\issue 4
\pages 703--749

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    This publication is cited in the following articles:
    1. E. D. Kosov, “Characterization of Besov classes in terms of a new modulus of continuity”, Dokl. Math., 96:3 (2017), 587–590  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    2. V. I. Bogachev, O. G. Smolyanov, Topological vector spaces and their applications, Springer Monographs in Mathematics, Springer, Cham, 2017, x+456 pp.  crossref  mathscinet  zmath  isi
    3. V. I. Bogachev, E. D. Kosov, S. N. Popova, “A characterization of Nikolskii–Besov classes via integration by parts”, Dokl. Math., 96:2 (2017), 449–453  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    4. Georgii I. Zelenov, “On distances between distributions of polynomials”, Theory Stoch. Process., 22(38):2 (2017), 79–85  mathnet  mathscinet  zmath
    5. V. I. Bogachev, E. D. Kosov, G. I. Zelenov, “Fractional smoothness of distributions of polynomials and a fractional analog of the Hardy-Landau-Littlewood inequality”, Trans. Amer. Math. Soc., 370:6 (2018), 4401–4432  crossref  mathscinet  zmath  isi  scopus
    6. V. I. Bogachev, “Ornstein–Uhlenbeck operators and semigroups”, Russian Math. Surveys, 73:2 (2018), 191–260  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. E. D. Kosov, “Besov classes on finite and infinite dimensional spaces”, Sb. Math., 210:5 (2019), 663–692  mathnet  crossref  crossref  adsnasa  isi  elib
    8. Bogachev I V., “Distributions of Polynomials in Many Variables and Nikolskii-Besov Spaces”, Real Anal. Exch., 44:1 (2019), 49–64  crossref  isi
    9. 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
    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
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