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Journal of Mathematical Sciences

, Volume 243, Issue 6, pp 907–916 | Cite as

The Bellman Function for a Parametric Family of Extremal Problems in BMO

  • N. N. OsipovEmail author
Article
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Let I be an interval of the real line and 〈⋅〉I be the corresponding integral average. We describe the behavior of the Bellman function for the functional F(φ) = 〈f ∘ φI, φ ∈ BMO(I), as f ranges over some parametric family of functions. Thereby, we once again demonstrate the power of the methods developed recently by V. I. Vasyunin, P. B. Zatitskiy, P. Ivanishvili, D. M. Stolyarov, and the author.

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References

  1. 1.
    P. Ivanishvili, N. N. Osipov, D. M. Stolyarov, V. I. Vasyunin, and P. B. Zatitskiy, “Bellman function for extremal problems in BMO,” Trans. Amer. Math. Soc., 368, 3415–3468 (2016).MathSciNetCrossRefGoogle Scholar
  2. 2.
    P. Ivanisvili, D. M. Stolyarov, V. I. Vasyunin, and P. B. Zatitskiy, Bellman Function for Extremal Problems in BMO II: Evolution, Memoirs Amer. Math. Soc., 255, No. 1220 (2018).Google Scholar
  3. 3.
    V. I. Vasyunin, “An example of the construction of a Bellman function for extremal problems in BMO space,” J. Math. Sci., 209, No. 5, 683–742 (2015).MathSciNetCrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.St. Petersburg Department of Steklov Institute of Mathematics and National Research University “Higher School of Economics”St. PetersburgRussia

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