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Bull. Korean Math. Soc. 2015; 52(3): 837-849

Printed May 31, 2015

https://doi.org/10.4134/BKMS.2015.52.3.837

Copyright © The Korean Mathematical Society.

Volume inequalities for the $L_p$-sine transform of isotropic measures

LuJun Guo and Gangsong Leng

Henan Normal University, Shanghai University

Abstract

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For $p\geq1$, sharp isoperimetric inequalities for the $L_p$-sine transform of isotropic measures are established. The corresponding reverse inequalities are obtained in an asymptotically optimal form. As applications of our main results, we present volume inequalities for convex bodies which are in $L_p$ surface isotropic position.

Keywords: isotropic measure, $L_p$-sine transform, Brascamp-Lieb inequality, reverse Brascamp-Lieb inequality, Urysohn inequality

MSC numbers: 52A20, 52A40

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