### 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) |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*359*(3), 1045-1079. https://doi.org/10.1090/S0002-9947-06-03939-0

**The surface measure and cone measure on the sphere of ℓ n
p
.** / Naor, Assaf.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 359, no. 3, pp. 1045-1079. https://doi.org/10.1090/S0002-9947-06-03939-0

}

TY - JOUR

T1 - The surface measure and cone measure on the sphere of ℓ n p

AU - Naor, Assaf

PY - 2007/3

Y1 - 2007/3

N2 - We prove a concentration inequality for the n p norm on the n psphere 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.

AB - We prove a concentration inequality for the n p norm on the n psphere 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.

KW - Concentration inequalities

KW - Cone measure

KW - Convex geometry.

KW - Geometry of

KW - Surface measure

UR - http://www.scopus.com/inward/record.url?scp=35548999999&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35548999999&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-06-03939-0

DO - 10.1090/S0002-9947-06-03939-0

M3 - Article

VL - 359

SP - 1045

EP - 1079

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 3

ER -