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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2021, Volume 498, Pages 27–30
DOI: https://doi.org/10.31857/S2686954321030061 (Mi danma172) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

On the Bellman function method for operators on martingales

V. A. Borovitskiiab, N. N. Osipovac, A. S. Tselishchevab

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b Chebyshev Laboratory, St. Petersburg State University, St. Petersburg, Russia
c International Laboratory of Game Theory and Decision Making, National Research University Higher School of Economics, St. Petersburg, Russia
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DOI: https://doi.org/10.31857/S2686954321030061
Abstract: It is shown how to apply the Bellman function method to general operators on martingales, i.e., to operators that are not necessarily martingale transforms. As examples of such operators, we consider the Haar transforms and an operator whose Lp-boundedness implies the Rubio de Francia inequality for the Walsh system. For the corresponding Bellman function, the Bellman induction is carried out and a Bellman candidate is constructed.
Keywords: Burkholder method, Gundy theorem, Walsh system, Rubio de Francia inequality, Haar transform.
Funding agency Grant number
Foundation for the Advancement of Theoretical Physics and Mathematics BASIS
HSE Academic Fund Programme
The work was supported by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”. The second author also acknowledges the support of the HSE University Basic Research Program.
Presented: S. V. Kislyakov
Received: 19.03.2021
Revised: 19.03.2021
Accepted: 06.04.2021
English version:
Doklady Mathematics, 2021, Volume 103, Issue 3, Pages 118–121
DOI: https://doi.org/10.1134/S1064562421030066
Bibliographic databases:
Document Type: Article
UDC: 519.216.8, 517.977.54, 517.983.23
Language: Russian
Citation: V. A. Borovitskii, N. N. Osipov, A. S. Tselishchev, “On the Bellman function method for operators on martingales”, Dokl. RAN. Math. Inf. Proc. Upr., 498 (2021), 27–30; Dokl. Math., 103:3 (2021), 118–121
Citation in format AMSBIB
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\paper On the Bellman function method for operators on martingales
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  • https://www.mathnet.ru/eng/danma172
  • https://www.mathnet.ru/eng/danma/v498/p27
    • This publication is cited in the following 1 articles:
    1. V. Borovitskiy, N. N. Osipov, A. Tselishchev, “Burkholder meets Gundy: Bellman function method for general operators on martingales”, Advances in Mathematics, 410 (2022), 108746  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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