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Fourier restriction theorems for curves with affine and Euclidean arclengths*

  • S. W. Drury (a1) and B. P. Marshall (a1)
Abstract

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].

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[2] W. F. Donoghue Jr. Monotone Matrix Functions and Analytic Continuation (Springer-Verlag, 1974).

[3] S. W. Drury . Restrictions of Fourier transforms to curves, to appear, Annales de l'institut Fourier, 35/1 (1985).

[4] C. Fefferman . Inequalities for strongly singular convolution operators. Acta Math. 124 (1970), 936.

[9] E. Prestini . A restriction theorem for space curves. Proc. Amer. Math. Soc. 70 (1978), 810.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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