The optimal hypercontractivity constant for a natural operator semigroup acting on a discrete finite probability space is established up to a universal factor. The two-point spaces are proved to be the extremal case. The constants obtained are also optimal in the related moment inequalities for sums of independent random variables.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-3-3,
author = {Pawe\l\ Wolff},
title = {Hypercontractivity of simple random variables},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {219-236},
zbl = {1133.60011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-3-3}
}
Paweł Wolff. Hypercontractivity of simple random variables. Studia Mathematica, Tome 178 (2007) pp. 219-236. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-3-3/