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

This article is cited in 7 scientific papers (total in 7 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).


DOI: https://doi.org/10.4213/rm9721

Full text: PDF file (859 kB)
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English version:
Russian Mathematical Surveys, 2016, 71:4, 703–749

Bibliographic databases:

Document Type: Article
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
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    Citing articles on Google Scholar: Russian citations, English citations
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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
    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, “Klassy Besova na konechnomernykh i beskonechnomernykh prostranstvakh”, Matem. sb., 210:5 (2019), 41–71  mathnet  crossref  elib
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