Riesz transforms on connected sums
Annales de l'Institut Fourier, Volume 57 (2007) no. 7, p. 2329-2343

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)

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).

DOI : https://doi.org/10.5802/aif.2334
Classification:  58J37,  58J35,  42B20
Keywords: Riesz transform, Sobolev inequalities
@article{AIF_2007__57_7_2329_0,
     author = {Carron, Gilles},
     title = {Riesz transforms on connected sums},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {57},
     number = {7},
     year = {2007},
     pages = {2329-2343},
     doi = {10.5802/aif.2334},
     mrnumber = {2394543},
     zbl = {1139.58020},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2007__57_7_2329_0}
}
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://www.numdam.org/item/AIF_2007__57_7_2329_0/

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