A new, rearrangement-free proof of the sharp hardy-littlewood-sobolev inequality

Rupert L. Frank, Elliott H. Lieb

Research output: Chapter in Book/Report/Conference proceedingChapter

34 Scopus citations

Abstract

We show that the sharp constant in the Hardy-Littlewood- Sobolev inequality can be derived using the method that we employe earlier for a similar inequality on the Heisenberg group. The merit of this proof is that it does not rely on rearrangement inequalities; it is the first one to do so for the whole parameter range.

Original languageEnglish (US)
Title of host publicationSpectral Theory, Function Spaces and Inequalities
Subtitle of host publicationNew Techniques and Recent Trends
PublisherSpringer Basel
Pages55-67
Number of pages13
ISBN (Electronic)9783034802635
ISBN (Print)9783034802628
DOIs
StatePublished - Jan 1 2012

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Hardy-Littlewood-Sobolev inequality
  • Sharp constants
  • Sobolev inequality

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    Frank, R. L., & Lieb, E. H. (2012). A new, rearrangement-free proof of the sharp hardy-littlewood-sobolev inequality. In Spectral Theory, Function Spaces and Inequalities: New Techniques and Recent Trends (pp. 55-67). Springer Basel. https://doi.org/10.1007/978-3-0348-0263-5