Riesz meets Sobolev

Details Riesz meets Sobolev Riesz meets Sobolev

2009-11-12

arxiv.org/abs/0911.2313v1

Mathematics

Analysis of PDEs

Scientific paper

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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