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

DOI:
https://doi.org/10.1090/S0002-9939-2012-11380-2

Published electronically:
April 5, 2012

MathSciNet review:
2957211

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Abstract | References | Similar Articles | Additional Information

Abstract: The sharp trace inequality of José Escobar is extended to traces for the fractional Laplacian on , 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:
https://doi.org/10.1090/S0002-9939-2012-11380-2

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.