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AN AFFINE FOURIER RESTRICTION THEOREM FOR CONICAL SURFACES
Published online by Cambridge University Press: 13 December 2013
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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- Research Article
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- Copyright
- Copyright © University College London 2013
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