Published 2012
| Updated
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A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality
- Creators
-
Frank, Rupert L.
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Lieb, Elliott H.
- Others:
- Brown, B. Malcolm
- Lang, Jan
- Wood, Ian G.
Chicago
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Abstract
We show that the sharp constant in the Hardy-Littlewood-Sobolev inequality can be derived using the method that we employed 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.
Additional Information
© 2012 Springer Basel AG. This paper may be reproduced, in its entirety, for non-commercial purposes. First Online: 11 October 2011. Support by U.S. NSF grant PHY 0965859 (E.H.L.) is acknowledged. We thank Richard Bamler for valuable help with Appendix B. The published version of this paper contains a typo in the following boxed formula (1.3), which has been corrected here. We thank T. Weth for pointing this out to us.Attached Files
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Additional details
- Eprint ID
- 77085
- DOI
- 10.1007/978-3-0348-0263-5_4
- Resolver ID
- CaltechAUTHORS:20170501-075729792
- NSF
- PHY-0965859
- Created
-
2017-05-01Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
- Series Name
- Operator Theory: Advances and Applications
- Series Volume or Issue Number
- 219