Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality

S. Artstein-Avidan; B. Klartag; C. Schütt; E. Werner

doi:10.1016/j.jfa.2012.02.014

Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality

S. Artstein-Avidan
, B. Klartag
, C. Schütt
, E. Werner

Tel Aviv University

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

Abstract

We give a functional version of the affine isoperimetric inequality for log-concave functions which may be interpreted as an inverse form of a logarithmic Sobolev inequality for entropy. A linearization of this inequality gives an inverse inequality to the Poincaré inequality for the Gaussian measure.

Original language	English
Pages (from-to)	4181-4204
Number of pages	24
Journal	Journal of Functional Analysis
Volume	262
Issue number	9
Early online date	28 Feb 2012
DOIs	https://doi.org/10.1016/j.jfa.2012.02.014
State	Published - 1 May 2012

Keywords

Affine isoperimetric inequality
Logarithmic Sobolev inequality

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2012.02.014

Cite this

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title = "Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality",

abstract = "We give a functional version of the affine isoperimetric inequality for log-concave functions which may be interpreted as an inverse form of a logarithmic Sobolev inequality for entropy. A linearization of this inequality gives an inverse inequality to the Poincar{\'e} inequality for the Gaussian measure.",

keywords = "Affine isoperimetric inequality, Logarithmic Sobolev inequality",

author = "S. Artstein-Avidan and B. Klartag and C. Sch{\"u}tt and E. Werner",

note = "Funding Information: * Corresponding author at: Department of Mathematics, Case Western Reserve University, Cleveland, OH 44106, USA. E-mail addresses: [email protected] (S. Artstein-Avidan), [email protected] (B. Klartag), [email protected] (C. Sch{\"u}tt), [email protected] (E. Werner). 1 Partially supported by BSF grant No. 2006079 and by ISF grant No. 865/07. 2 Partially supported by an ISF grant and an IRG grant. 3 Partially supported by NSF grant and BSF grant No. 2006079.",

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doi = "10.1016/j.jfa.2012.02.014",

language = "English",

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T1 - Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality

AU - Artstein-Avidan, S.

AU - Klartag, B.

AU - Schütt, C.

AU - Werner, E.

N1 - Funding Information: * Corresponding author at: Department of Mathematics, Case Western Reserve University, Cleveland, OH 44106, USA. E-mail addresses: [email protected] (S. Artstein-Avidan), [email protected] (B. Klartag), [email protected] (C. Schütt), [email protected] (E. Werner). 1 Partially supported by BSF grant No. 2006079 and by ISF grant No. 865/07. 2 Partially supported by an ISF grant and an IRG grant. 3 Partially supported by NSF grant and BSF grant No. 2006079.

PY - 2012/5/1

Y1 - 2012/5/1

N2 - We give a functional version of the affine isoperimetric inequality for log-concave functions which may be interpreted as an inverse form of a logarithmic Sobolev inequality for entropy. A linearization of this inequality gives an inverse inequality to the Poincaré inequality for the Gaussian measure.

AB - We give a functional version of the affine isoperimetric inequality for log-concave functions which may be interpreted as an inverse form of a logarithmic Sobolev inequality for entropy. A linearization of this inequality gives an inverse inequality to the Poincaré inequality for the Gaussian measure.

KW - Affine isoperimetric inequality

KW - Logarithmic Sobolev inequality

UR - https://www.scopus.com/pages/publications/84857912067

U2 - 10.1016/j.jfa.2012.02.014

DO - 10.1016/j.jfa.2012.02.014

M3 - Article

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VL - 262

SP - 4181

EP - 4204

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 9

ER -

Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality

Abstract

Keywords

ASJC Scopus subject areas

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