Comptes Rendus
no. 5
Mathematical Analysis/Partial Differential Equations
Multilinear estimates for the Laplace spectral projectors on compact manifolds
Presented by: Yves Meyer
Nicolas Burq1; Patrick Gérard1; Nikolay Tzvetkov1
1Université Paris Sud, mathématiques, bâtiment 425, 91405 Orsay cedex, France
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

Nicolas Burq  1 ; Patrick Gérard  1 ; Nikolay Tzvetkov  1

1 Université Paris Sud, mathématiques, bâtiment 425, 91405 Orsay cedex, France 
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Nicolas Burq; Patrick Gérard; Nikolay Tzvetkov. 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

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