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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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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

  • eBook Packages: Springer Book Archive