Sharp Results in the Integral-form John–nirenberg Inequality
نویسنده
چکیده
We consider the strong form of the John-Nirenberg inequality for the L2-based BMO. We construct explicit Bellman functions for the inequality in the continuous and dyadic settings and obtain the sharp constant, as well as the precise bound on the inequality’s range of validity, both previously unknown. The results for the two cases are substantially different. The paper not only gives another instance in the short list of such explicit calculations, but also presents the Bellman function method as a sequence of clear steps, adaptable to a wide variety of applications.
منابع مشابه
The John–Nirenberg inequality with sharp constants Meilleures constantes dans l’inégalité de John–Nirenberg
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. ©...
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