Harmonic Analysis
The John–Nirenberg inequality with sharp constants
Comptes Rendus. Mathématique, Volume 351 (2013) no. 11-12, pp. 463-466.

We consider the one-dimensional John–Nirenberg inequality:

A. Korenovskii found that the sharp C2 here is C2=2/e. It is shown in this paper that if C2=2/e, then the best possible C1 is C1=12e4/e.

On considère lʼinégalité de John–Nirenberg unidimensionnelle :

A. Korenovskii a montré que la meilleure constante C2 était égale à 2/e. Dans cette Note, on montre que si C2=2/e, alors la meilleure constante possible pour C1 est C1=12e4/e.

Published online:
DOI: 10.1016/j.crma.2013.07.007
Lerner, Andrei K. 1

1 Department of Mathematics, Bar-Ilan University, 5290002 Ramat Gan, Israel
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     title = {The {John{\textendash}Nirenberg} inequality with sharp constants},
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Lerner, Andrei K. The John–Nirenberg inequality with sharp constants. Comptes Rendus. Mathématique, Volume 351 (2013) no. 11-12, pp. 463-466. doi : 10.1016/j.crma.2013.07.007. http://www.numdam.org/articles/10.1016/j.crma.2013.07.007/

[1] John, F.; Nirenberg, L. On functions of bounded mean oscillation, Commun. Pure Appl. Math., Volume 14 (1961), pp. 415-426

[2] Hytönen, T. The A2 theorem: Remarks and complements (preprint, available at) | arXiv

[3] Klemes, I. A mean oscillation inequality, Proc. Amer. Math. Soc., Volume 93 (1985) no. 3, pp. 497-500

[4] Korenovskii, A.A. The connection between mean oscillations and exact exponents of summability of functions, Mat. Sb., Volume 181 (1990) no. 12, pp. 1721-1727 (in Russian); translation in Math. USSR-Sb., 71, 2, 1992, pp. 561-567

[5] Korenovskii, A.A. Mean Oscillations and Equimeasurable Rearrangements of Functions, Lect. Notes Unione Mat. Ital., vol. 4, Springer/UMI, Berlin/Bologna, 2007

[6] Lerner, A.K. A pointwise estimate for local sharp maximal function with applications to singular integrals, Bull. London Math. Soc., Volume 42 (2010) no. 5, pp. 843-856

[7] 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

[8] Vasyunin, V.; Volberg, A. Sharp constants in the classical weak form of the John–Nirenberg inequality (preprint, available at) | arXiv

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