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

74 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

Access to Document

10.1007/s00526-009-0302-x

Cite this

@article{3cfd053ff5df4496b83eb20b5b14539a,

title = "Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality",

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.",

author = "Frank, {Rupert L.} and Lieb, {Elliott H.}",

year = "2010",

doi = "10.1007/s00526-009-0302-x",

language = "English (US)",

volume = "39",

pages = "85--99",

journal = "Calculus of Variations and Partial Differential Equations",

issn = "0944-2669",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality

AU - Frank, Rupert L.

AU - Lieb, Elliott H.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77954426563&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954426563&partnerID=8YFLogxK

U2 - 10.1007/s00526-009-0302-x

DO - 10.1007/s00526-009-0302-x

M3 - Article

AN - SCOPUS:77954426563

SN - 0944-2669

VL - 39

SP - 85

EP - 99

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 1

ER -

Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this