Restrictions of Fourier transforms to curves
Annales de l'Institut Fourier, Volume 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 Cf a for f𝒮(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 Cf a pour f𝒮(R 3). Le résultat améliore un ancien théorème de restriction de Prestini. Ce résultat est généralisé dans certaines directions.

@article{AIF_1985__35_1_117_0,
     author = {Drury, S. W.},
     title = {Restrictions of {Fourier} transforms to curves},
     journal = {Annales de l'Institut Fourier},
     pages = {117--123},
     publisher = {Institut Fourier},
     volume = {35},
     number = {1},
     year = {1985},
     doi = {10.5802/aif.1001},
     zbl = {0548.42008},
     mrnumber = {86e:42026},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1001/}
}
TY  - JOUR
AU  - Drury, S. W.
TI  - Restrictions of Fourier transforms to curves
JO  - Annales de l'Institut Fourier
PY  - 1985
DA  - 1985///
SP  - 117
EP  - 123
VL  - 35
IS  - 1
PB  - Institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.1001/
UR  - https://zbmath.org/?q=an%3A0548.42008
UR  - https://www.ams.org/mathscinet-getitem?mr=86e:42026
UR  - https://doi.org/10.5802/aif.1001
DO  - 10.5802/aif.1001
LA  - en
ID  - AIF_1985__35_1_117_0
ER  - 
%0 Journal Article
%A Drury, S. W.
%T Restrictions of Fourier transforms to curves
%J Annales de l'Institut Fourier
%D 1985
%P 117-123
%V 35
%N 1
%I Institut Fourier
%U https://doi.org/10.5802/aif.1001
%R 10.5802/aif.1001
%G en
%F AIF_1985__35_1_117_0
Drury, S. W. Restrictions of Fourier transforms to curves. Annales de l'Institut Fourier, Volume 35 (1985) no. 1, pp. 117-123. doi : 10.5802/aif.1001. http://www.numdam.org/articles/10.5802/aif.1001/

[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. | MR | Zbl

[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. | MR | Zbl

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

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

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

[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. | MR | Zbl

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

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

Cited by Sources: