Email this article The Bellman Function for a Parametric Family of Extremal Problems in BMO
- Authors: Osipov N.N.1
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Affiliations:
- St. Petersburg Department of Steklov Institute of Mathematics and National Research University “Higher School of Economics”
- Issue: Vol 243, No 6 (2019)
- Pages: 907-916
- Section: Article
- URL: https://ogarev-online.ru/1072-3374/article/view/243183
- DOI: https://doi.org/10.1007/s10958-019-04591-5
- ID: 243183
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Abstract
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.
About the authors
N. N. Osipov
St. Petersburg Department of Steklov Institute of Mathematics and National Research University “Higher School of Economics”
Author for correspondence.
Email: nicknick@pdmi.ras.ru
Russian Federation, St. Petersburg
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