TY - JOUR
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 - http://www.scopus.com/inward/record.url?scp=84857912067&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2012.02.014
DO - 10.1016/j.jfa.2012.02.014
M3 - مقالة
SN - 0022-1236
VL - 262
SP - 4181
EP - 4204
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 9
ER -