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AN AFFINE FOURIER RESTRICTION THEOREM FOR CONICAL SURFACES

Published online by Cambridge University Press:  13 December 2013

Jonathan Hickman*
Affiliation:
The School of Mathematics, The University of Edinburgh, Room 5409, James Clerk Maxwell Building, King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ,U.K. email j.e.hickman@sms.ed.ac.uk

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.

Type
Research Article
Copyright
Copyright © University College London 2013 

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