  We generalize the Stein-Tomas [17] $L^2$-restricition theorem and the uniform
Sobolev estimates of Kenig, Ruiz and the second author [11] by allowing
critically singular potential. We also obtain Strichartz estimates for
Schr\"odinger and wave operators with such potentials. Due to the fact that
there may be nontrivial eigenfunctions we are required to make certain spectral
assumptions, such as assuming that the solutions only involve sufficiently
large frequencies.
