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Algebra i Analiz, 2024, Volume 36, Issue 4, Pages 57–147 (Mi aa1929)  

Research Papers

Sharp bounds for distribution of martingale transform of bounded functions

M. I. Novikov

Saint Petersburg State University
References:
Abstract: The paper suggests a characterization of positive function $ f $ such that $ f(\psi_\infty) $ is summable for any limit value $ \psi_\infty $ of the martingale transform for an indicator function. The characterizing condition is that a version of the Lipschitz majorant of $ f $ is summable with respect to an exponential weight. The reasoning is based on the calculation of particular minimal biconcave functions on the strip.
Keywords: Burkholder's method, biconcave functions, Bellman function, martingale transform, Stein–Weiss formula.
Funding agency Grant number
Russian Science Foundation 19-71-10023
Received: 11.03.2024
Document Type: Article
Language: Russian
Citation: M. I. Novikov, “Sharp bounds for distribution of martingale transform of bounded functions”, Algebra i Analiz, 36:4 (2024), 57–147
Citation in format AMSBIB
\Bibitem{Nov24}
\by M.~I.~Novikov
\paper Sharp bounds for distribution of martingale transform of bounded functions
\jour Algebra i Analiz
\yr 2024
\vol 36
\issue 4
\pages 57--147
\mathnet{http://mi.mathnet.ru/aa1929}
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  • https://www.mathnet.ru/eng/aa1929
  • https://www.mathnet.ru/eng/aa/v36/i4/p57
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    Алгебра и анализ St. Petersburg Mathematical Journal
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    References:27
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