Sobolev inequalities for probability measures on the real line

F. Barthe, and C. Roberto. "Sobolev inequalities for probability measures on the real line." Studia Mathematica 159.3 (2003): 481-497. <http://eudml.org/doc/285321>.

@article{F2003,
abstract = {We give a characterization of those probability measures on the real line which satisfy certain Sobolev inequalities. Our starting point is a simpler approach to the Bobkov-Götze characterization of measures satisfying a logarithmic Sobolev inequality. As an application of the criterion we present a soft proof of the Latała-Oleszkiewicz inequality for exponential measures, and describe the measures on the line which have the same property. New concentration inequalities for product measures follow.},
author = {F. Barthe, C. Roberto},
journal = {Studia Mathematica},
keywords = {concentration; Poincaré inequalities; optimal constants},
language = {eng},
number = {3},
pages = {481-497},
title = {Sobolev inequalities for probability measures on the real line},
url = {http://eudml.org/doc/285321},
volume = {159},
year = {2003},
}

TY - JOUR
AU - F. Barthe
AU - C. Roberto
TI - Sobolev inequalities for probability measures on the real line
JO - Studia Mathematica
PY - 2003
VL - 159
IS - 3
SP - 481
EP - 497
AB - We give a characterization of those probability measures on the real line which satisfy certain Sobolev inequalities. Our starting point is a simpler approach to the Bobkov-Götze characterization of measures satisfying a logarithmic Sobolev inequality. As an application of the criterion we present a soft proof of the Latała-Oleszkiewicz inequality for exponential measures, and describe the measures on the line which have the same property. New concentration inequalities for product measures follow.
LA - eng
KW - concentration; Poincaré inequalities; optimal constants
UR - http://eudml.org/doc/285321
ER -