Open Access
Article

Positivity

, Volume 16, Issue 2, pp 359-371

Khinchine type inequalities with optimal constants via ultra log-concavity

Authors

  • Piotr Nayar
    • Institute of MathematicsUniversity of Warsaw
  • Krzysztof Oleszkiewicz
    • Institute of MathematicsUniversity of Warsaw
    • Institute of MathematicsPolish Academy of Sciences

DOI: 10.1007/s11117-011-0130-z

Abstract

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.

Keywords

Log-concavity Ultra log-concavity Khinchine inequality Factorial moments

Mathematics Subject Classification (2000)

60E15 26D15

Acknowledgments

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.

Copyright information

© The Author(s) 2011