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Weighted Restriction for Curves

Published online by Cambridge University Press:  20 November 2018

Joseph D. Lakey
Joseph D. Lakey*
Affiliation:
Department of Mathematics The University of Texas Austin, Texas 78712 U.S.A.
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Abstract

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We prove weighted norm inequalities for the Fourier transform of the form

where v is a nonnegative weight function on ℝd and ψ: [— 1,1 ] —> ℝd is a nondegenerate curve. Our results generalize unweighted (i.e. v = 1) restriction theorems of M. Christ, and two-dimensional weighted restriction theorems of C. Carton-Lebrun and H. Heinig.

Keywords

42B10Fourier transformrestriction theoremsweighted norm inequalities
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 1 , 01 March 1993 , pp. 87 - 95
Copyright
Copyright © Canadian Mathematical Society 1993

References

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