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:

|{xI0:|f(x)fI0|>α}|C1|I0|exp(C2fα).
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 :

|{xI0:|f(x)fI0|>α}|C1|I0|exp(C2fα).
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.

Received:
Accepted:
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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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/

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