Restriction for flat surfaces of revolution in ${\mathbf R}^3$

We investigate restriction theorems for hypersurfaces of revolution in $\mathbf{R}^3,$ with affine curvature introduced as a mitigating factor. Abi-Khuzam and Shayya recently showed that a Stein-Tomas restriction theorem can be obtained for a class of convex hypersurfaces that includes the surfaces $\Gamma(x)=(x,e^{-1/\vert x\vert^m}), m\geq 1.$ We enlarge their class of hypersurfaces and give a much simplified proof of their result.