  We prove an endpoint version of the Stein-Tomas restriction theorem, for a
general class of measures, and with a strengthened Lorentz space estimate. A
similar improvement is obtained for Stein's estimate on oscillatory integrals
of Carleson-Sj\"olin-H\"ormander type and some spectral projection operators on
compact manifolds, and for classes of oscillatory integral operators with
one-sided fold singularities.
