A Fourier restriction estimate is obtained for a broad class of conic surfaces by adding a weight to the usual underlying measure. The new restriction estimate exhibits a certain affine- invariance and implies the sharp L-p - L-q restriction theorem for compact subsets of a type k conical surface, up to an endpoint. Furthermore, the chosen weight is shown to be, in some quantitative sense, optimal. Appended is a discussion of type k conical restriction theorems which addresses some anomalies present in the existing literature.
- DEGENERATE CURVES