no. 7
Riesz transforms on connected sums
[Transformée de Riesz sur les sommes connexes]
Carron, Gilles1
1 Université de Nantes Laboratoire de Mathématiques Jean Leray (UMR 6629) 2, rue de la Houssinière B.P. 92208 44322 Nantes Cedex 3 (France)
Annales de l'Institut Fourier, Tome 57 (2007) no. 7, pp. 2329-2343.

Soit M 0 une variété riemannienne complète à courbure de Ricci bornée inférieurement et qui vérifie l’inégalité Sobolev de dimension ν>3. Si M est une variété riemannienne complète isométrique à M 0 en dehors d’un compact et si p∈(ν/(ν-1),ν) alors lorsque la transformée de Riesz est bornée sur L p (M 0 ) elle est également bornée sur L p (M).

Assume that M 0 is a complete Riemannian manifold with Ricci curvature bounded from below and that M 0 satisfies a Sobolev inequality of dimension ν>3. Let M be a complete Riemannian manifold isometric at infinity to M 0 and let p∈(ν/(ν-1),ν). The boundedness of the Riesz transform of L p (M 0 ) then implies the boundedness of the Riesz transform of L p (M)

DOI : 10.5802/aif.2334
Classification : 58J37, 58J35, 42B20
Keywords: Riesz transform, Sobolev inequalities
Mot clés : transformée de Riesz, inégalités de Sobolev

Carron, Gilles 1

1 Université de Nantes Laboratoire de Mathématiques Jean Leray (UMR 6629) 2, rue de la Houssinière B.P. 92208 44322 Nantes Cedex 3 (France) 
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Carron, Gilles. Riesz transforms on connected sums. Annales de l'Institut Fourier, Tome 57 (2007) no. 7, pp. 2329-2343. doi : 10.5802/aif.2334. https://aif.centre-mersenne.org/articles/10.5802/aif.2334/

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