Mathematical Analysis/Partial Differential Equations
Multilinear estimates for the Laplace spectral projectors on compact manifolds
Comptes Rendus. Mathématique, Volume 338 (2004) no. 5, pp. 359-364.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2003.12.015
Burq, Nicolas 1; Gérard, Patrick 1; Tzvetkov, Nikolay 1

1 Université Paris Sud, mathématiques, bâtiment 425, 91405 Orsay cedex, France
@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, Volume 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] Burq, N.; Gérard, P.; Tzvetkov, N. Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces (Preprint, 2003) | arXiv

[2] Gallot, S.; Hulin, D.; Lafontaine, J. Riemannian Geometry, Universitext, Springer-Verlag, Berlin, 1990

[3] Hörmander, L. Oscillatory integrals and multipliers on FLp, Ark. Math., Volume 11 (1973), pp. 1-11

[4] Sogge, C. Oscillatory integrals and spherical harmonics, Duke Math. J., Volume 53 (1986), pp. 43-65

[5] Sogge, C. 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] Sogge, C. Fourier Integrals in Classical Analysis, Cambridge Tracts in Math., 1993

[7] Stein, E.M. Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Monographs Harmon. Anal., III, Princeton University Press, Princeton, NJ, 1993

Cited by Sources: