no. 11-12
Mathematical Analysis/Partial Differential Equations
On Bellman function for extremal problems in BMO
[Sur la fonction de Bellman pour des problèmes extrémaux sur lʼespace BMO]

Présenté par : Gilles Pisier

Ivanishvili, Paata1, 2 ; Osipov, Nikolay N.1, 3 ; Stolyarov, Dmitriy M.1, 3 ; Vasyunin, Vasily I.3 ; Zatitskiy, Pavel B.1, 3
1 Chebyshev Laboratory (SPbU), 14th Line 29B, Vasilyevsky Island, St. Petersburg, Russia
2 Saint Petersburg State University, Universitetsky prospekt 28, Peterhof, St. Petersburg, Russia
3 St. Petersburg Department of Steklov Mathematical Institute RAS, Fontanka 27, St. Petersburg, Russia
Comptes Rendus. Mathématique, Tome 350 (2012) no. 11-12, pp. 561-564.

Dans cette Note, nous décrivons nos résultats sur la construction de la fonction de Bellman qui résout un problème extrémal pour une grande classe de formes linéaires intégrales sur BMO.

In this Note we describe our results on construction of the Bellman function solving an extremal problem for a large class of integral functionals on BMO.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.06.011
Ivanishvili, Paata 1, 2 ; Osipov, Nikolay N. 1, 3 ; Stolyarov, Dmitriy M. 1, 3 ; Vasyunin, Vasily I. 3 ; Zatitskiy, Pavel B. 1, 3

1 Chebyshev Laboratory (SPbU), 14th Line 29B, Vasilyevsky Island, St. Petersburg, Russia
2 Saint Petersburg State University, Universitetsky prospekt 28, Peterhof, St. Petersburg, Russia
3 St. Petersburg Department of Steklov Mathematical Institute RAS, Fontanka 27, St. Petersburg, Russia 
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     author = {Ivanishvili, Paata and Osipov, Nikolay N. and Stolyarov, Dmitriy M. and Vasyunin, Vasily I. and Zatitskiy, Pavel B.},
     title = {On {Bellman} function for extremal problems in {BMO}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {561--564},
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Ivanishvili, Paata; Osipov, Nikolay N.; Stolyarov, Dmitriy M.; Vasyunin, Vasily I.; Zatitskiy, Pavel B. On Bellman function for extremal problems in BMO. Comptes Rendus. Mathématique, Tome 350 (2012) no. 11-12, pp. 561-564. doi : 10.1016/j.crma.2012.06.011. http://www.numdam.org/articles/10.1016/j.crma.2012.06.011/

[1] Ivanishvili, P.; Osipov, N.; Stolyarov, D.; Vasyunin, V.; Zatitskiy, P. Bellman function for extremal problems in BMO, 2012 (preprint) | arXiv

[2] Slavin, L.; Vasyunin, V. Sharp Lp estimates on BMO, 2011 (preprint) | arXiv

[3] Slavin, L.; Vasyunin, V. Sharp results in the integral-form John–Nirenberg inequality, Trans. Amer. Math. Soc., Volume 363 (2011) no. 8, pp. 4135-4169 (preprint, 2007) | arXiv

[4] Vasyunin, V. The sharp constant in the John–Nirenberg inequality, 2003 http://www.pdmi.ras.ru/preprint/2003/index.html (preprint POMI, No. 20)

[5] Vasyunin, V.I. Mutual estimates of Lp-norms, and the Bellman function, Zapiski POMI, Volume 355 (2008) no. 5, pp. 81-138 (in Russian); English translation in: J. Math. Sci., 156, 2009, pp. 766-798

[6] Vasyunin, V. Sharp constants in the classical weak form of the John–Nirenberg inequality, 2011 http://www.pdmi.ras.ru/preprint/2011/eng-2011.html (preprint POMI, No. 10)

[7] Vasyunin, Vasily; Volberg, Alexander Monge–Ampère equation and Bellman optimization of Carleson embedding theorems, Amer. Math. Soc. Transl. Ser. 2, Volume 226 (2009), pp. 195-238

[8] Vasyunin, Vasily; Volberg, Alexander Sharp constants in the classical weak form of the John–Nirenberg inequality, 2012 (preprint) | arXiv

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