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Published 2012 | Updated
Book Section - Chapter Open

A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality

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.

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