A sharp analog of Young's inequality on S N and related entropy inequalities

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

Research output: Contribution to journalArticlepeer-review

69 Scopus citations


We prove a sharp analog of Young's inequality on S N, 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 R N to more than three functions, and leads to significant new information about the optimizers and the constants.

Original languageEnglish (US)
Pages (from-to)487-520
Number of pages34
JournalJournal of Geometric Analysis
Issue number3
StatePublished - 2004

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


  • Inequalities
  • best constants
  • entropy
  • optimizers


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