On the distribution of random variables corresponding to Musielak-Orlicz norms

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Autor/in:
Erscheinungsjahr:
2013
Medientyp:
Text
Schlagworte:
  • Inequality
  • Log-concave
  • Convex body
  • Computational Geometry
  • Convex Body
  • Algorithms
  • Inequality
  • Log-concave
  • Convex body
  • Computational Geometry
  • Convex Body
  • Algorithms
Beschreibung:
  • as Given a normalized Orlicz function M we provide an easy formula for a distribution such that, if X is a random variable distributed accordingly and X-1, ... ,X-n are independent copies of X, then 1/Cp parallel to x parallel to(M) <= E parallel to(x(i)X(i))(i=1)(n) parallel to(p) <= C-p parallel to x parallel to (M), where C-p is a positive constant depending only on p. In case p = 2 we need the function t bar right arrow tM'(t)-M(t) to be 2-concave and as an application immediately obtain an embedding of the corresponding Orlicz spaces into L-1{[}0,1]. We also provide a general result replacing the l(p)-norm by an arbitrary N-norm. This complements some deep results obtained by Gordon, Litvak, Schiitt, and Werner {[}Ann. Prob. 30 (2002)]. We also prove, in the spirit of that paper, a result which is of a simpler form and easier to apply. All results are true in the more general setting of Musielak-Orlicz spaces.
Lizenz:
  • info:eu-repo/semantics/restrictedAccess
Quellsystem:
Forschungsinformationssystem der UHH

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oai:www.edit.fis.uni-hamburg.de:publications/311d2013-464f-4cc8-96ec-6547c0db39a9