Sharp results in the integral-form John--Nirenberg inequality
Classical Analysis and ODEs
2011-10-11 v2
Abstract
We consider the strong form of the John-Nirenberg inequality for the -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.
Keywords
Cite
@article{arxiv.0709.4332,
title = {Sharp results in the integral-form John--Nirenberg inequality},
author = {L. Slavin and V. Vasyunin},
journal= {arXiv preprint arXiv:0709.4332},
year = {2011}
}
Comments
37 pages, 8 figures, final version; Trans. Amer. Math. Soc., Vol. 363, No. 8 (2011)