Sharp trace inequalities for fractional Laplacians

Einav, Amit; Loss, Michael

doi:10.1090/S0002-9939-2012-11380-2

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.

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