no. 1
Restrictions of Fourier transforms to curves
Annales de l'Institut Fourier, Tome 35 (1985) no. 1, pp. 117-123

Let x(t)=(t,1 2t 2 ,1 6t 3 ) a certain curve in R 3 . We investigate inequalities of the type {∫|f ^(x(t))| b dt} 1/b ≤C∥f∥ a for f∈𝒮(R 3). Our results improve improve an earlier restriction theorem of Prestini. Various generalizations are also discussed.

Soitx(t)=(t,1 2t 2 ,1 6t 3 ) une certaine courbe dans R 3 . On étudie les inégalités de la forme {∫|f ^(x(t))| b dt} 1/b ≤C∥f∥ a pour f∈𝒮(R 3). Le résultat améliore un ancien théorème de restriction de Prestini. Ce résultat est généralisé dans certaines directions.

Drury, S. W. Restrictions of Fourier transforms to curves. Annales de l'Institut Fourier, Tome 35 (1985) no. 1, pp. 117-123. doi: 10.5802/aif.1001
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[1] E.M. Stein, Harmonic Analysis on Rn, Studies in Harmonic Analysis, 97-135, The Mathematical Association of America Studies in Mathematics vol. 13, 1976. | Zbl | MR

[2] P.A. Thomas, Restriction theorems for the Fourier Transform, Proceedings of Symposia in Pure Mathematics, vol. 35 part 1 (1979), 111-114, AMS, Providence. | Zbl | MR

[3] E. Prestini, A restriction theorem for space curves, Proc. A.M.S., 70 (1978), 8-10. | Zbl | MR

[4] H.W. Guggenheimer, Differential Geometry, Dover, New York, 1977. | Zbl | MR

[5] A. Zygmund, On Fourier coefficients and transforms of functions of two variables, Studia Math., 50 (1974), 189-201. | Zbl | MR

[6] A. Benedeck and R. Panzone, The Lp spaces with mixed norm, Duke Math J., 28 (1961), 301-324. | Zbl

[7] E.M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton U.P., Princeton 1971. | Zbl | MR

[8] R.A. Hunt, On L(p, q) spaces, L'Ens. Math., 12 (1966), 249-275. | Zbl | MR

[9] G. Polya and G. Szegö, Problems and Theorems in Analysis, Springer-Verlag, New York, 1976.

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