Riesz meets Sobolev

Thierry Coulhon, and Adam Sikora. "Riesz meets Sobolev." Colloquium Mathematicae 118.2 (2010): 685-704. <http://eudml.org/doc/284020>.

@article{ThierryCoulhon2010,
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.},
author = {Thierry Coulhon, Adam Sikora},
journal = {Colloquium Mathematicae},
keywords = {Riesz transform; Sobolev type inequality; heat kernel; Riemannian manifold},
language = {eng},
number = {2},
pages = {685-704},
title = {Riesz meets Sobolev},
url = {http://eudml.org/doc/284020},
volume = {118},
year = {2010},
}

TY - JOUR
AU - Thierry Coulhon
AU - Adam Sikora
TI - Riesz meets Sobolev
JO - Colloquium Mathematicae
PY - 2010
VL - 118
IS - 2
SP - 685
EP - 704
AB - 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.
LA - eng
KW - Riesz transform; Sobolev type inequality; heat kernel; Riemannian manifold
UR - http://eudml.org/doc/284020
ER -