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

Rupert L. Frank; Elliott H. Lieb

doi:10.1007/978-3-0348-0263-5

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

Rupert L. Frank, Elliott H. Lieb

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

68 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 language	English (US)
Title of host publication	Spectral Theory, Function Spaces and Inequalities
Subtitle of host publication	New Techniques and Recent Trends
Publisher	Springer Basel
Pages	55-67
Number of pages	13
ISBN (Electronic)	9783034802635
ISBN (Print)	9783034802628
DOIs	https://doi.org/10.1007/978-3-0348-0263-5
State	Published - Jan 1 2012

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Hardy-Littlewood-Sobolev inequality
Sharp constants
Sobolev inequality

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10.1007/978-3-0348-0263-5

Cite this

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KW - Sharp constants

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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