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http://dx.doi.org/10.4134/BKMS.2015.52.3.837

VOLUME INEQUALITIES FOR THE Lp-SINE TRANSFORM OF ISOTROPIC MEASURES  

Guo, LuJun (College of Mathematics and Information Science Henan Normal University)
Leng, Gangsong (Department of Mathematics Shanghai University)
Publication Information
Bulletin of the Korean Mathematical Society / v.52, no.3, 2015 , pp. 837-849 More about this Journal
Abstract
For $p{\geq}1$, 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;
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