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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A restriction theorem for space curves


Author: E. Prestini
Journal: Proc. Amer. Math. Soc. 70 (1978), 8-10
MSC: Primary 42A68
DOI: https://doi.org/10.1090/S0002-9939-1978-0467160-6
MathSciNet review: 0467160
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Abstract: Let $ \alpha $ be a $ {C^k}$ curve $ (k \geqslant 3)$ in $ {R^3}$ with nonvanishing curvature and torsion. It is proved that the restriction operator $ T:f \to \hat f{\vert _\alpha }$ is bounded from $ {L^p}({R^3})$ to $ {L^q}(\alpha )$ if $ 1 \leqslant p < 15/13$ and $ 1/q > 6(1 - 1/p)$, and that T is not bounded if $ p \geqslant 6/5$ or $ 1/q < 6(1 - 1/p)$.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0467160-6
Article copyright: © Copyright 1978 American Mathematical Society