The surface measure and cone measure on the sphere of ℓ np

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We prove a concentration inequality for the np norm on the npsphere 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 languageEnglish (US)
Pages (from-to)1045-1079
Number of pages35
JournalTransactions of the American Mathematical Society
Issue number3
StatePublished - Mar 1 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics


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


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