no. 3-4
Number Theory
Bounds on oscillatory integral operators
[Estimées sur les integrales oscillatoires]

Présenté par : Jean Bourgain

Bourgain, Jean1 ; Guth, Lawrence1
1 Institute for Advanced Study, School of Mathematics, 1 Einstein Drive, Princeton, NJ 08540, USA
Comptes Rendus. Mathématique, Tome 349 (2011) no. 3-4, pp. 137-141.

Nous présentons de nouvelles estimations dans le problème de E. Stein sur la restriction de Fourier à des hyper-surfaces à courbure dans Rn ainsi que sur les intégrales oscillatoires introduites par L. Hörmander.

We present new estimates in E. Stein's Fourier restriction problem for curved hyper-surfaces in Rn and also on the mapping properties of the more general class of oscillatory integral operators introduced by L. Hörmander.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.12.004
Bourgain, Jean 1 ; Guth, Lawrence 1

1 Institute for Advanced Study, School of Mathematics, 1 Einstein Drive, Princeton, NJ 08540, USA 
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Bourgain, Jean; Guth, Lawrence. Bounds on oscillatory integral operators. Comptes Rendus. Mathématique, Tome 349 (2011) no. 3-4, pp. 137-141. doi : 10.1016/j.crma.2010.12.004. http://www.numdam.org/articles/10.1016/j.crma.2010.12.004/

[1] Bennett, J.; Carbery, T.; Tao, T. On the multilinear restriction and Kakeya conjectures, Acta Math., Volume 196 (2006), pp. 261-302

[2] Bourgain, J. Some new estimates on oscillatory integrals, Annals Math. St., vol. 42, Princeton University Press, 1995, pp. 83-112

[3] Stein, E. Oscillatory integrals in Fourier analysis, Beijing Lectures in Harmonic Analysis, Annals Math. St., vol. 112, Princeton University Press, 1986

[4] Tao, T. A sharp bilinear restriction estimate for the paraboloids, GAFA, Volume 13 (2003), pp. 1359-1384

[5] Wolff, T. An improved bound for Kakeya-type maximal functions, Rev. Mat. Iber., Volume 11 (1995) no. 3, pp. 651-674

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