  Multilinear embedding estimates for the fractional Laplacian are obtained in
terms of functionals defined over a hyperbolic surface. Convolution estimates
used in the proof enlarge the classical framework of the convolution algebra
for Riesz potentials to include the critical endpoint index, and provide new
realizations for fractional integral inequalities that incorporate restriction
to smooth submanifolds. Results developed here are modeled on the space-time
estimate used by Klainerman and Machedon in their proof of uniqueness for the
Gross-Pitaevskii hierarchy.
