We prove estimates in hyperbolic Sobolev spaces H-s,H-delta(R1+d), d >= 3, for velocity averages over spheres of solutions to the kinetic transport equation partial derivative(t)f + v . del(x)f = Omega(i,j)(v) g, where Omega(i,j)(v) g are tangential velocity derivatives of g. Our results extend to all dimensions earlier results of Bournaveas and Perthame in dimension two [J. Math. Pures Appl., 9 (2001), pp. 517-534]. We construct counterexamples to test the optimality of our results.