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Stochastic Inequalities and Applications pp 157–168Cite as

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On a Nonsymmetric Version of the Khinchine-Kahane Inequality

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Part of the Progress in Probability book series (PRPR,volume 56)

Abstract

We prove a new version of the Khinchine—Kahane inequality in which Bernoulli random variables no longer need to be symmetric. The constant in the inequality is optimal up to some universal factor. The proof uses hypercontractive methods and the optimal hypercontractivity constant for a mean-zero Bernoulli random variable is found. A simple observation generalizing Pisier’s Rademacher projection norm estimate is added.

Key words and phrases

  • Bernoulli distribution
  • hypercontractivity
  • moment inequality
  • random vector
  • Rademacher projection.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Krzysztof Oleszkiewicz

Authors
  1. Krzysztof Oleszkiewicz
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Editor information

Editors and Affiliations

  1. Department of Mathematics, U-3009, University of Connecticut, Storrs, CT, 06268, USA

    Evariste Giné

  2. Laboratoire d’Analyse et de Mathématiques Appliquées CNRS UMR 8050, Université de Paris XII, 94010, Créteil Cedex, France

    Christian Houdré

  3. Georgia Institute of Technology, School of Mathematics, Atlanta, GA, 30332, USA

    Christian Houdré

  4. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via, 585, 08007, Barcelona, Spain

    David Nualart

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Oleszkiewicz, K. (2003). On a Nonsymmetric Version of the Khinchine-Kahane Inequality. In: Giné, E., Houdré, C., Nualart, D. (eds) Stochastic Inequalities and Applications. Progress in Probability, vol 56. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8069-5_11

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  • DOI: https://doi.org/10.1007/978-3-0348-8069-5_11

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9428-9

  • Online ISBN: 978-3-0348-8069-5

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