, Volume 16, Issue 2, pp 359–371 | Cite as

Khinchine type inequalities with optimal constants via ultra log-concavity

  • Piotr Nayar
  • Krzysztof Oleszkiewicz
Open Access


We derive Khinchine type inequalities for even moments with optimal constants from the result of Walkup (J Appl Probab 13:76–85, 1976) which states that the class of log-concave sequences is closed under the binomial convolution.


Log-concavity Ultra log-concavity Khinchine inequality Factorial moments 

Mathematics Subject Classification (2000)

60E15 26D15 



We are grateful to Matthieu Fradelizi and Olivier Guédon for pointing to us the article of Walkup, and for their help in tracing some other references.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of WarsawWarsawPoland
  2. 2.Institute of MathematicsPolish Academy of SciencesWarsawPoland

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