Geodesic
Riesz meets Sobolev
Thierry Coulhon 1   ; Adam Sikora 2
1 Département de Mathématiques Université de Cergy-Pontoise Site de Saint-Martin 2, rue Adolphe Chauvin F-95302 Cergy-Pontoise Cedex, France
2 Department of Mathematics Macquarie University Sydney, NSW 2109, Australia
Colloquium Mathematicum, Tome 118 (2010) no. 2, pp. 685-704 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We show that the $L^p$ boundedness, $p>2$, of the Riesz transform on a complete non-compact Riemannian manifold with upper and lower Gaussian heat kernel estimates is equivalent to a certain form of Sobolev inequality. We also characterize in such terms the heat kernel gradient upper estimate on manifolds with polynomial growth.
DOI : 10.4064/cm118-2-20
Keywords: boundedness riesz transform complete non compact riemannian manifold upper lower gaussian heat kernel estimates equivalent certain form sobolev inequality characterize terms heat kernel gradient upper estimate manifolds polynomial growth

Thierry Coulhon  1   ; Adam Sikora  2

1 Département de Mathématiques Université de Cergy-Pontoise Site de Saint-Martin 2, rue Adolphe Chauvin F-95302 Cergy-Pontoise Cedex, France
2 Department of Mathematics Macquarie University Sydney, NSW 2109, Australia 
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Thierry Coulhon; Adam Sikora. Riesz meets Sobolev. Colloquium Mathematicum, Tome 118 (2010) no. 2, pp. 685-704. doi: 10.4064/cm118-2-20

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