The surface measure and cone measure on the sphere of lpn

被引：77
作者：
Naor, Assaf
机构：
[1] Microsoft Res, Redmond, WA 98052 USA
[2] Hebrew Univ Jerusalem, Dept Math, Jerusalem, Israel
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2007年 / 359卷 / 03期
关键词：
geometry of l(p)(n); cone measure; surface measure; concentration inequalities; convex geometry;
D O I：
10.1090/S0002-9947-06-03939-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove a concentration inequality for the l(q)(n) norm on the l(p)(n) sphere for p, q > 0. This inequality, which generalizes results of Schechtman and Zinn ( 2000), is used to study the distance between the cone measure and surface measure on the sphere of l(p)(n). In particular, we obtain a significant strengthening of the inequality derived by Naor and Romik ( 2003), and calculate the precise dependence of the constants that appeared there on p.
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收藏
页码：1045 / 1079
页数：35
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