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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 sharpL   p   ‐    L   qrestriction 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.

AN AFFINE FOURIER RESTRICTION THEOREM FOR CONICAL SURFACES