Riesz transforms on connected sums

Gilles Carron[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)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 7, page 2329-2343
  • ISSN: 0373-0956

Abstract

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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 )

How to cite

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Carron, Gilles. "Riesz transforms on connected sums." Annales de l’institut Fourier 57.7 (2007): 2329-2343. <http://eudml.org/doc/10298>.

@article{Carron2007,
abstract = {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 $\nu &gt;3$. Let $M$ be a complete Riemannian manifold isometric at infinity to $M_0$ and let $p\in (\nu /(\nu -1), \nu )$. The boundedness of the Riesz transform of $L^p(M_0)$ then implies the boundedness of the Riesz transform of $L^p(M)$},
affiliation = {Université de Nantes Laboratoire de Mathématiques Jean Leray (UMR 6629) 2, rue de la Houssinière B.P. 92208 44322 Nantes Cedex 3 (France)},
author = {Carron, Gilles},
journal = {Annales de l’institut Fourier},
keywords = {Riesz transform; Sobolev inequalities; Riemannian manifold},
language = {eng},
number = {7},
pages = {2329-2343},
publisher = {Association des Annales de l’institut Fourier},
title = {Riesz transforms on connected sums},
url = {http://eudml.org/doc/10298},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Carron, Gilles
TI - Riesz transforms on connected sums
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 7
SP - 2329
EP - 2343
AB - 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 $\nu &gt;3$. Let $M$ be a complete Riemannian manifold isometric at infinity to $M_0$ and let $p\in (\nu /(\nu -1), \nu )$. The boundedness of the Riesz transform of $L^p(M_0)$ then implies the boundedness of the Riesz transform of $L^p(M)$
LA - eng
KW - Riesz transform; Sobolev inequalities; Riemannian manifold
UR - http://eudml.org/doc/10298
ER -

References

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