AN AFFINE FOURIER RESTRICTION THEOREM FOR CONICAL SURFACES

Jonathan Hickman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)374-390
Number of pages17
JournalMathematika
Volume60
Issue number2
DOIs
Publication statusPublished - Jul 2014

Keywords

  • DEGENERATE CURVES
  • R-3
  • TRANSFORM
  • HYPERSURFACES
  • CONJECTURE
  • REVOLUTION
  • R2

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