Riesz transforms on connected sums

Carron, Gilles

Riesz transforms on connected sums
[Transformée de Riesz sur les sommes connexes]

Carron, Gilles

Annales de l'Institut Fourier, Tome 57 (2007), p. 2329-2343 / Harvested from Numdam

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Résumé
Abstract

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 $p \in (ν / (ν - 1), ν)$ 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 $p \in (ν / (ν - 1), ν)$ . The boundedness of the Riesz transform of $L^{p} (M_{0})$ then implies the boundedness of the Riesz transform of $L^{p} (M)$

Publié le : 2007-01-01

MR 2394543 | Zbl 1139.58020

DOI : https://doi.org/10.5802/aif.2334
Classification: 58J37, 58J35, 42B20
Mots clés: transformée de Riesz, inégalités de Sobolev

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     author = {Carron, Gilles},
     title = {Riesz transforms on connected sums},
     journal = {Annales de l'Institut Fourier},
     volume = {57},
     year = {2007},
     pages = {2329-2343},
     doi = {10.5802/aif.2334},
     zbl = {1139.58020},
     mrnumber = {2394543},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2007__57_7_2329_0}
}

Carron, Gilles. Riesz transforms on connected sums. Annales de l'Institut Fourier, Tome 57 (2007) pp. 2329-2343. doi : 10.5802/aif.2334. http://gdmltest.u-ga.fr/item/AIF_2007__57_7_2329_0/

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