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

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作者：

Osipov N.N. ^{[1
]}

机构：

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

来源：

Journal of Mathematical Sciences | 2019年 / 243卷 / 6期

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D O I：

10.1007/s10958-019-04591-5

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摘要：

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 ∘ φ〉I, 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. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

引用

页码：907 / 916

页数：9

共 3 条

[1] Ivanishvili P., Osipov N.N., Stolyarov D.M., Vasyunin V.I., Zatitskiy P.B., Bellman function for extremal problems in BMO, Trans. Amer. Math. Soc., 368, pp. 3415-3468, (2016)
[2] Ivanisvili P., Stolyarov D.M., Vasyunin V.I., Zatitskiy P.B., Bellman Function for Extremal Problems in BMO II: Evolution, Memoirs Amer. Math. Soc., 255, 1220, (2018)
[3] Vasyunin V.I., An example of the construction of a Bellman function for extremal problems in BMO space, J. Math. Sci., 209, 5, pp. 683-742, (2015)

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