Sharp trace inequalities for fractional Laplacians
Sharp trace inequalities for fractional Laplacians
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.