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VOLUME INEQUALITIES FOR THE Lp-SINE TRANSFORM OF ISOTROPIC MEASURES

  • Guo, LuJun ;
  • Leng, Gangsong
  • Received : 2014.03.18
  • Published : 2015.05.31

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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  1. Optimal Sobolev norms in the affine class vol.436, pp.1, 2016, https://doi.org/10.1016/j.jmaa.2015.11.063

Acknowledgement

Supported by : National Natural Science Foundation of China