The Lp Loomis-Whitney inequality

Ai-Jun Li Henan Polytechnic University Qingzhong Huang Jiaxing University

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.
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  title={The Lp  Loomis-Whitney inequality},
  author={Ai-Jun Li, and Qingzhong Huang},
  booktitle={Advances in Applied Mathematics},
Ai-Jun Li, and Qingzhong Huang. The Lp Loomis-Whitney inequality. 2016. Vol. 75. In Advances in Applied Mathematics. pp.94-115.
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