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

Bar-Ilan University

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

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

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1016/j.crma.2013.07.007

Cite this

@article{a0506efdfab641b3882b64d8a3677581,

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.",

author = "Lerner, \{Andrei K.\}",

year = "2013",

month = jun,

doi = "10.1016/j.crma.2013.07.007",

language = "الإنجليزيّة",

volume = "351",

pages = "463--466",

number = "11-12",

}

TY - JOUR

T1 - The John-Nirenberg inequality with sharp constants

AU - Lerner, Andrei K.

PY - 2013/6

Y1 - 2013/6

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84881610647&partnerID=8YFLogxK

U2 - 10.1016/j.crma.2013.07.007

DO - 10.1016/j.crma.2013.07.007

M3 - مقالة

SN - 1631-073X

VL - 351

SP - 463

EP - 466

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 11-12

ER -

The John-Nirenberg inequality with sharp constants

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this