Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality

Rupert L. Frank; Elliott H. Lieb

doi:10.1007/s00526-009-0302-x

Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality

Rupert L. Frank
, Elliott H. Lieb

Mathematics

Research output: Contribution to journal › Article › peer-review

86 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	85-99
Number of pages	15
Journal	Calculus of Variations and Partial Differential Equations
Volume	39
Issue number	1
DOIs	https://doi.org/10.1007/s00526-009-0302-x
State	Published - 2010

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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abstract = "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.",

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AU - Lieb, Elliott H.

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Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality

Abstract

All Science Journal Classification (ASJC) codes

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