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Zapiski Nauchnykh Seminarov POMI, 2023, Volume 527, Pages 5–53 (Mi znsl7388)  
This article is cited in 3 scientific papers (total in 3 papers)

Some extremal problems for martingale transforms. I

V. I. Vasyunina, P. B. Zatitskiiab

a Saint Petersburg State University
b University of Cincinnati
Full-text PDF (1017 kB) Citations (3)
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Abstract: With this paper, we begin a series of studies of extremal problems for estimating the distributions of martingale transforms of bounded martingales. The Bellman functions corresponding to such problems are pointwise minimal diagonally concave functions on a horizontal strip, satisfying certain given boundary conditions. We describe the basic structures that arise in the construction such functions and present a solution in the case \break of asymmetric boundary conditions and a sufficiently small width of the strip.
Key words and phrases: Bellman function, martingale transform, diagonally concave function.
Funding agency Grant number
Russian Science Foundation 19-71-10023
Received: 25.10.2023
English version:
Journal of Mathematical Sciences (New York), 2024, Volume 284, Issue 6, Pages 735–766
DOI: https://doi.org/10.1007/s10958-024-07387-4
Document Type: Article
UDC: 517.51, 519.216.8
Language: Russian
Citation: V. I. Vasyunin, P. B. Zatitskii, “Some extremal problems for martingale transforms. I”, Investigations on linear operators and function theory. Part 51, Zap. Nauchn. Sem. POMI, 527, POMI, St. Petersburg, 2023, 5–53; J. Math. Sci. (N. Y.), 284:6 (2024), 735–766
Citation in format AMSBIB
\Bibitem{VasZat23}
\by V.~I.~Vasyunin, P.~B.~Zatitskii
\paper Some extremal problems for martingale transforms. I
\inbook Investigations on linear operators and function theory. Part~51
\serial Zap. Nauchn. Sem. POMI
\yr 2023
\vol 527
\pages 5--53
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7388}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2024
\vol 284
\issue 6
\pages 735--766
\crossref{https://doi.org/10.1007/s10958-024-07387-4}
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