The John-Nirenberg inequality with sharp constants

Andrei K. Lerner

The John-Nirenberg inequality with sharp constants

Classical Analysis and ODEs 2013-03-15 v1

Authors: Andrei K. Lerner

Abstract

We consider the one-dimensional John-Nirenberg inequality: $|\{x\in I_0:|f(x)-f_{I_0}|>\a\}|\le C_1|I_0|\exp\Big(-\frac{C_2}{\|f\|_{*}}\a\Big).$ A. Korenovskii found that the sharp $C_2$ here is $C_2=2/e$ . It is shown in this paper that if $C_2=2/e$ , then the best possible $C_1$ is $C_1= \frac{1}{2}e^{4/e}$ .

Cite

@article{arxiv.1303.3310,
  title  = {The John-Nirenberg inequality with sharp constants},
  author = {Andrei K. Lerner},
  journal= {arXiv preprint arXiv:1303.3310},
  year   = {2013}
}

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