Sharp trace inequalities for fractional Laplacians
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- by Amit Einav and Michael Loss PDF
- Proc. Amer. Math. Soc. 140 (2012), 4209-4216 Request permission
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.References
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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
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 4209-4216
- MSC (2010): Primary 35A23
- DOI: https://doi.org/10.1090/S0002-9939-2012-11380-2
- MathSciNet review: 2957211