Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Fourier restriction theorems for curves with affine and Euclidean arclengths*

S. W. Drurya1 and B. P. Marshalla1

a1 Department of Mathematics, McGill University, Montreal, P.Q. H3A 2K6, Canada

Let M be a smooth manifold in S0305004100062654_inline1. One may ask whether S0305004100062654_inline2, the restriction of the Fourier transform of f to M makes sense for every f in S0305004100062654_inline3. Since, for S0305004100062654_inline4 does not make sense pointwise, it is natural to introduce a measure σ on M and ask for an inequality

S0305004100062654_eqnU1

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].

(Received June 08 1984)

Footnotes

* Both authors are supported by grants from NSERC Canada.