We establish a family of sharp Sobolev trace inequalities involving the
Wk,2(R+n+1β,ya)-norm. These inequalities are closely related
to the realization of fractional powers of the Laplacian on
Rn=βR+n+1β as generalized Dirichlet-to-Neumann
operators associated to powers of the weighted Laplacian in upper half space,
generalizing observations of Caffarelli--Silvestre and of Yang.Comment: 25 page