The John-Nirenberg inequality with sharp constants

Andrei K. Lerner

doi:10.1016/j.crma.2013.07.007

The John-Nirenberg inequality with sharp constants

Andrei K. Lerner

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

We consider the one-dimensional John-Nirenberg inequality:|{x∈I0:|f(x)-fI0|>α}|≤C1|I0|exp(-C2f*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=12e4/e.

Original language	English
Pages (from-to)	463-466
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	351
Issue number	11-12
DOIs	https://doi.org/10.1016/j.crma.2013.07.007
State	Published - Jun 2013

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title = "The John-Nirenberg inequality with sharp constants",

abstract = "We consider the one-dimensional John-Nirenberg inequality:|{x∈I0:|f(x)-fI0|>α}|≤C1|I0|exp(-C2f*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=12e4/e.",

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AB - We consider the one-dimensional John-Nirenberg inequality:|{x∈I0:|f(x)-fI0|>α}|≤C1|I0|exp(-C2f*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=12e4/e.

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ER -

The John-Nirenberg inequality with sharp constants

Abstract

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