Sharp results in the integral-form John--Nirenberg inequality

Details Sharp results in the integral-form John--Nirenberg inequality Sharp results in the integral-form John--Nirenberg inequality

2007-09-27

arxiv.org/abs/0709.4332v2

Mathematics

Classical Analysis and ODEs

37 pages, 8 figures, final version; Trans. Amer. Math. Soc., Vol. 363, No. 8 (2011)

Scientific paper

We consider the strong form of the John-Nirenberg inequality for the $L^2$-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.

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