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Fourier restriction theorems for curves with affine and Euclidean arclengths*

Published online by Cambridge University Press:  24 October 2008

S. W. Drury  and
B. P. Marshall
S. W. Drury
Affiliation:
Department of Mathematics, McGill University, Montreal, P.Q. H3A 2K6, Canada
B. P. Marshall
Affiliation:
Department of Mathematics, McGill University, Montreal, P.Q. H3A 2K6, Canada
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Extract

Let M be a smooth manifold in . One may ask whether , the restriction of the Fourier transform of f to M makes sense for every f in . Since, for does not make sense pointwise, it is natural to introduce a measure σ on M and ask for an inequality

for every f in (say) the Schwartz class. Results of this kind are called restriction theorems. An excellent survey article on this subject is to be found in Tomas[13].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 1 , January 1985 , pp. 111 - 125
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

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