## Abstract

We prove a concentration inequality for the ^{n}_{p} norm on the ^{n}_{p}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 ^{n} _{p}. 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.

Original language | English (US) |
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Pages (from-to) | 1045-1079 |

Number of pages | 35 |

Journal | Transactions of the American Mathematical Society |

Volume | 359 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2007 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

## Keywords

- Concentration inequalities
- Cone measure
- Convex geometry.
- Geometry of
- Surface measure

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