Published September 2010
| Version Published + Submitted
Journal Article
Open
Inversion positivity and the sharp Hardy–Littlewood–Sobolev inequality
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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.
Additional Information
© 2009 The Authors. This paper may be reproduced, in its entirety, for non-commercial purposes. Received: 28 April 2009; Accepted: 25 November 2009; First Online: 23 December 2009. We are grateful to E. Carlen for pointing out that the conformal invariance of the HLS functional and the conventional reflection positivity through planes imply the inversion positivity through spheres. This allows us to circumvent our original, direct but complicated proof, which uses properties of Gegenbauer polynomials. Support through DFG grant FR 2664/1-1 (R.F.) and U.S. NSF grant PHY 0652854 (R.F. and E.L.) is gratefully acknowledged.Attached Files
Published - art_3A10.1007_2Fs00526-009-0302-x.pdf
Submitted - 0904.4275.pdf
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0904.4275.pdf
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Additional details
Identifiers
- Eprint ID
- 77354
- Resolver ID
- CaltechAUTHORS:20170510-143424777
Related works
- Describes
- https://arxiv.org/abs/0904.4275 (URL)
Funding
- Deutsche Forschungsgemeinschaft (DFG)
- FR 2664/1-1
- NSF
- PHY-0652854
Dates
- Created
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2017-05-12Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field