Sharp trace inequalities for fractional Laplacians

Einav, Amit ; Loss, Michael (2012-04-05)


The sharp trace inequality of José Escobar is extended to traces for the fractional Laplacian on Rⁿ 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.