A restriction theorem for space curves
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- by E. Prestini PDF
- Proc. Amer. Math. Soc. 70 (1978), 8-10 Request permission
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 $T:f \to \hat f{|_\alpha }$ 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 $1/q < 6(1 - 1/p)$.References
- Charles Fefferman, Inequalities for strongly singular convolution operators, Acta Math. 124 (1970), 9–36. MR 257819, DOI 10.1007/BF02394567
- Charles Fefferman, A note on spherical summation multipliers, Israel J. Math. 15 (1973), 44–52. MR 320624, DOI 10.1007/BF02771772
- Lennart Carleson and Per Sjölin, Oscillatory integrals and a multiplier problem for the disc, Studia Math. 44 (1972), 287–299. (errata insert). MR 361607, DOI 10.4064/sm-44-3-287-299
- Per Sjölin, Fourier multipliers and estimates of the Fourier transform of measures carried by smooth curves in $R^{2}$, Studia Math. 51 (1974), 169–182. MR 385437, DOI 10.4064/sm-51-2-169-182 L. Hörmander, Oscillatory integrals and multipliers on $F{L^p}$, Ark. Mat. 11 (1973), 1-11.
- Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972
Additional Information
- © Copyright 1978 American Mathematical Society
- 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