Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality

Rupert L. Frank, Elliott H. Lieb

Research output: Contribution to journalArticlepeer-review

69 Scopus citations


We give a new proof of certain cases of the sharp HLS inequality. Instead of symmetric decreasing rearrangement it uses the reflection positivity of inversions in spheres. In doing this we extend a characterization of the minimizing functions due to Li and Zhu.

Original languageEnglish (US)
Pages (from-to)85-99
Number of pages15
JournalCalculus of Variations and Partial Differential Equations
Issue number1
StatePublished - 2010

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


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