181 citations · 194 across the 12 of their papers we have counts for
17 papers
Riesz transforms for bounded Laplacians on graphs
Li Chen, Thierry Coulhon, Bobo Hua
We study several problems related to the boundedness of Riesz transforms for graphs endowed with so-called bounded Laplacians. Introducing a proper notion of gradient of f…
Gradient estimates for heat kernels and harmonic functions
Thierry Coulhon, Renjin Jiang, Pekka Koskela +1
Let be a doubling metric measure space endowed with a Dirichlet form $\E$ deriving from a "carré du champ". Assume that $(X,d,μ,\E)$ supports a scale-invariant -Poin…
Gaussian heat kernel estimates: from functions to forms
Thierry Coulhon, Baptiste Devyver, Adam Sikora
On a complete non-compact Riemannian manifold satisfying the volume doubling property, we give conditions on the negative part of the Ricci curvature that ensure that, unless there…
Sobolev Algebra Counterexamples
Thierry Coulhon, Luke G. Rogers
In the Euclidean setting the Sobolev spaces are algebras for the pointwise product when and . This property has recently been extended…
Regularisation effects of nonlinear semigroups
Thierry Coulhon, Daniel Hauer
One introduces natural and simple methods to deduce --re\-gularisation estimates for of nonlinear semigroups holding uniformly for all time with…
Riesz transform for without Gaussian heat kernel bound
Li Chen, Thierry Coulhon, Joseph Feneuil +1
We study the boundedness of Riesz transform as well as the reverse inequality on Riemannian manifolds and graphs under the volume doubling property and a sub-Gaussian heat ke…