Riesz transform on manifolds and heat kernel regularity

@article{Auscher2004RieszTO,
  title={Riesz transform on manifolds and heat kernel regularity},
  author={Pascal Auscher and T. Coulhon and Xuan Thinh Duong and S. Hofmann},
  journal={Annales Scientifiques De L Ecole Normale Superieure},
  year={2004},
  volume={37},
  pages={911-957}
}
  • Pascal Auscher, T. Coulhon, +1 author S. Hofmann
  • Published 2004
  • Mathematics
  • Annales Scientifiques De L Ecole Normale Superieure
  • Abstract One considers the class of complete non-compact Riemannian manifolds whose heat kernel satisfies Gaussian estimates from above and below. One shows that the Riesz transform is L p bounded on such a manifold, for p ranging in an open interval above 2, if and only if the gradient of the heat kernel satisfies a certain L p estimate in the same interval of p's. 
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