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Convex and Discrete Geometry mathscidoc:1703.40022

Advances in Applied Mathematics, 75, 94-115, 2016
In this paper, we establish the $L_p$ Loomis-Whitney inequality for even isotropic measures in terms of the support function of $L_p$ projection bodies with complete equality conditions. This generalizes Ball's Loomis-Whitney inequality to the $L_p$ setting. In addition, the sharp upper bound of the minimal $p$-mean width of $L_p$ zonoids is obtained.
$L_p$ Loomis-Whitney inequality, $L_p$ zonoid, $L_p$ projection body, generalized $\ell_p^n$-ball.
@inproceedings{ai-jun2016the,
title={The Lp  Loomis-Whitney inequality},
author={Ai-Jun Li, and Qingzhong Huang},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170304091158945141608},