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A sharp analog of Young’s inequality on SN and related entropy inequalities

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Abstract

We prove a sharp analog of Young’s inequality on SN, and deduce from it certain sharp entropy inequalities. The proof turns on constructing a nonlinear heat flow that drives trial functions to optimizers in a monotonic manner. This strategy also works for the generalization of Young’s inequality on RN to more than three functions, and leads to significant new information about the optimizers and the constants.

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Authors and Affiliations

  1. School of Mathematics, Georgia Tech, 30332, Atlanta, GA

    E. A. Carlen, E. H. Lieb & M. Loss

  2. Departments of Mathematics and Physics, Princeton University, Jadwin Hall, P.O. Box 708, 08544, Princeton, NJ

    E. A. Carlen, E. H. Lieb & M. Loss

Authors
  1. E. A. Carlen
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  2. E. H. Lieb
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  3. M. Loss
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Communicated by Steven Krantz

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Carlen, E.A., Lieb, E.H. & Loss, M. A sharp analog of Young’s inequality on SN and related entropy inequalities. J Geom Anal 14, 487–520 (2004). https://doi.org/10.1007/BF02922101

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  • DOI: https://doi.org/10.1007/BF02922101

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