Riesz meets Sobolev
Analysis of PDEs
2009-11-13 v1
Abstract
We show that the boundedness, , 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.
Cite
@article{arxiv.0911.2313,
title = {Riesz meets Sobolev},
author = {Thierry Coulhon and Adam Sikora},
journal= {arXiv preprint arXiv:0911.2313},
year = {2009}
}