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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Sharp trace inequalities for fractional Laplacians


Authors: Amit Einav and Michael Loss
Journal: Proc. Amer. Math. Soc. 140 (2012), 4209-4216
MSC (2010): Primary 35A23
Published electronically: April 5, 2012
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Abstract: The sharp trace inequality of José Escobar is extended to traces for the fractional Laplacian on $ \mathbb{R}^n$, and a complete characterization of cases of equality is discussed. The proof proceeds via Fourier transform and uses Lieb's sharp form of the Hardy-Littlewood-Sobolev inequality.


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Additional Information

Amit Einav
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160
Email: aeinav@math.gatech.edu

Michael Loss
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160
Email: loss@math.gatech.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11380-2
PII: S 0002-9939(2012)11380-2
Received by editor(s): May 20, 2011
Published electronically: April 5, 2012
Additional Notes: The authors were supported in part by NSF grant DMS-0901304.
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.