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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm159-3-9,
author = {F. Barthe and C. Roberto},
title = {Sobolev inequalities for probability measures on the real line},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {481-497},
zbl = {1072.60008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm159-3-9}
}
F. Barthe; C. Roberto. Sobolev inequalities for probability measures on the real line. Studia Mathematica, Tome 157 (2003) pp. 481-497. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm159-3-9/