The John–Nirenberg inequality with sharp constants Meilleures constantes dans l’inégalité de John–Nirenberg
نویسنده
چکیده
Article history: Received 14 March 2013 Accepted after revision 3 July 2013 Available online 29 July 2013 Presented by Yves Meyer We consider the one-dimensional John–Nirenberg inequality: ∣∣{x ∈ I0: ∣∣ f (x)− f I0 ∣∣>α}∣∣ C1|I0|exp ( − C2 ‖ f ‖∗ α ) . 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 = 2 e4/e. © 2013 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved. r é s u m é On considère l’inégalité de John–Nirenberg unidimensionnelle : ∣∣{x ∈ I0: ∣∣ f (x)− f I0 ∣∣>α}∣∣ C1|I0|exp ( − C2 ‖ f ‖∗ α ) . 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 = 2 e4/e. © 2013 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved.
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