[Estimées multilinéaires pour les projecteurs spectraux du laplacien sur les variétés compactes]
L'objet de cette Note est de généraliser à toute dimension d'espace les estimations bilinéaires de projecteurs spectraux de l'opérateur de Laplace sur une variété compacte (sans bord), démontrées par les auteurs (preprint : http://www.arxiv.org/abs/math/0308214) en dimension 2. On énonce aussi des estimations trilinéaires.
The purpose of this Note is to extend to any space dimension the bilinear estimate for eigenfunctions of the Laplace operator on a compact manifold (without boundary) obtained by the authors (preprint: http://www.arxiv.org/abs/math/0308214) in dimension 2. We also give some related trilinear estimates.
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@article{CRMATH_2004__338_5_359_0,
author = {Burq, Nicolas and G\'erard, Patrick and Tzvetkov, Nikolay},
title = {Multilinear estimates for the {Laplace} spectral projectors on~compact manifolds},
journal = {Comptes Rendus. Math\'ematique},
pages = {359--364},
publisher = {Elsevier},
volume = {338},
number = {5},
year = {2004},
doi = {10.1016/j.crma.2003.12.015},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2003.12.015/}
}
TY - JOUR AU - Burq, Nicolas AU - Gérard, Patrick AU - Tzvetkov, Nikolay TI - Multilinear estimates for the Laplace spectral projectors on compact manifolds JO - Comptes Rendus. Mathématique PY - 2004 SP - 359 EP - 364 VL - 338 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2003.12.015/ DO - 10.1016/j.crma.2003.12.015 LA - en ID - CRMATH_2004__338_5_359_0 ER -
%0 Journal Article %A Burq, Nicolas %A Gérard, Patrick %A Tzvetkov, Nikolay %T Multilinear estimates for the Laplace spectral projectors on compact manifolds %J Comptes Rendus. Mathématique %D 2004 %P 359-364 %V 338 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2003.12.015/ %R 10.1016/j.crma.2003.12.015 %G en %F CRMATH_2004__338_5_359_0
Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay. Multilinear estimates for the Laplace spectral projectors on compact manifolds. Comptes Rendus. Mathématique, Tome 338 (2004) no. 5, pp. 359-364. doi : 10.1016/j.crma.2003.12.015. http://www.numdam.org/articles/10.1016/j.crma.2003.12.015/
[1] Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces (Preprint, 2003) | arXiv
[2] Riemannian Geometry, Universitext, Springer-Verlag, Berlin, 1990
[3] Oscillatory integrals and multipliers on FLp, Ark. Math., Volume 11 (1973), pp. 1-11
[4] Oscillatory integrals and spherical harmonics, Duke Math. J., Volume 53 (1986), pp. 43-65
[5] Concerning the Lp norm of spectral clusters for second order elliptic operators on compact manifolds, J. Funct. Anal., Volume 77 (1988), pp. 123-138
[6] Fourier Integrals in Classical Analysis, Cambridge Tracts in Math., 1993
[7] Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Monographs Harmon. Anal., III, Princeton University Press, Princeton, NJ, 1993
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