Comptes Rendus
no. 3-4
Number Theory
Bounds on oscillatory integral operators

Presented by: Jean Bourgain

Jean Bourgain1; Lawrence Guth1
1 Institute for Advanced Study, School of Mathematics, 1 Einstein Drive, Princeton, NJ 08540, USA
Comptes Rendus. Mathématique, Volume 349 (2011) no. 3-4, pp. 137-141.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2010.12.004

Jean Bourgain 1; Lawrence Guth 1

1 Institute for Advanced Study, School of Mathematics, 1 Einstein Drive, Princeton, NJ 08540, USA 
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Jean Bourgain; Lawrence Guth. Bounds on oscillatory integral operators. Comptes Rendus. Mathématique, Volume 349 (2011) no. 3-4, pp. 137-141. doi : 10.1016/j.crma.2010.12.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.12.004/

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

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

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

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

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

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