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arXiv · 0911.2313

Riesz meets Sobolev

Thierry Coulhon·Adam Sikora
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Abstract

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.

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Thierry Coulhon, Adam Sikora. 2009-11-12. Riesz meets Sobolev. https://arxiv.org/abs/0911.2313

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