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Riesz meets Sobolev

Coulhon, Thierry; Sikora, Adam


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.

CollectionsANU Research Publications
Date published: 2010
Type: Journal article
Source: Colloquium Mathematicum
DOI: 10.4064/cm118-2-20


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