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arXiv · 1307.3735

An affine Fourier restriction theorem for conical surfaces

Jonathan Hickman
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Abstract

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.

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Jonathan Hickman. 2013-07-14. An affine Fourier restriction theorem for conical surfaces. https://doi.org/10.1112/s002557931300020x

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