Riesz meets Sobolev
Thierry Coulhon ; Adam Sikora
Colloquium Mathematicae, Tome 120 (2010), p. 685-704 / Harvested from The Polish Digital Mathematics Library
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We show that the Lp 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.

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:284020 
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     title = {Riesz meets Sobolev},
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     volume = {120},
     year = {2010},
     pages = {685-704},
     zbl = {1194.58027},
     language = {en},
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Thierry Coulhon; Adam Sikora. Riesz meets Sobolev. Colloquium Mathematicae, Tome 120 (2010) pp. 685-704. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-2-20/