Assume that is a complete Riemannian manifold with Ricci curvature bounded from below and that satisfies a Sobolev inequality of dimension . Let be a complete Riemannian manifold isometric at infinity to and let . The boundedness of the Riesz transform of then implies the boundedness of the Riesz transform of
Soit une variété riemannienne complète à courbure de Ricci bornée inférieurement et qui vérifie l’inégalité Sobolev de dimension . Si est une variété riemannienne complète isométrique à en dehors d’un compact et si alors lorsque la transformée de Riesz est bornée sur elle est également bornée sur .
Keywords: Riesz transform, Sobolev inequalities
Mot clés : transformée de Riesz, inégalités de Sobolev
@article{AIF_2007__57_7_2329_0, author = {Carron, Gilles}, title = {Riesz transforms on connected sums}, journal = {Annales de l'Institut Fourier}, pages = {2329--2343}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {57}, number = {7}, year = {2007}, doi = {10.5802/aif.2334}, zbl = {1139.58020}, mrnumber = {2394543}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2334/} }
TY - JOUR AU - Carron, Gilles TI - Riesz transforms on connected sums JO - Annales de l'Institut Fourier PY - 2007 SP - 2329 EP - 2343 VL - 57 IS - 7 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2334/ DO - 10.5802/aif.2334 LA - en ID - AIF_2007__57_7_2329_0 ER -
Carron, Gilles. Riesz transforms on connected sums. Annales de l'Institut Fourier, Volume 57 (2007) no. 7, pp. 2329-2343. doi : 10.5802/aif.2334. http://archive.numdam.org/articles/10.5802/aif.2334/
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