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Some extensions of the Prékopa–Leindler inequality using Borell’s stochastic approach

Volume 238 / 2017

Dario Cordero-Erausquin, Bernard Maurey Studia Mathematica 238 (2017), 201-233 MSC: Primary 39B62; Secondary 52A40, 60H30, 52A20. DOI: 10.4064/sm8515-10-2016 Published online: 28 April 2017

Abstract

We present an abstract form of the Prékopa–Leindler inequality that includes several known—and a few new—related functional inequalities on Euclidean spaces. The method of proof and also the formulation of the new inequalities are based on Christer Borell’s stochastic approach to Brunn–Minkowski type inequalities.

Authors

  • Dario Cordero-ErausquinInstitut de Mathématiques de Jussieu-PRG
    UPMC (Paris 6)
    F-75252 Paris Cedex 05, France
    e-mail
  • Bernard MaureyInstitut de Mathématiques de Jussieu-PRG
    UPMC (Paris 6)
    F-75252 Paris Cedex 05, France

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