57 citations · 57 across the 3 of their papers we have counts for
6 papers
On necessary and sufficient conditions for -estimates of Riesz transforms associated to elliptic operators on $\RR^n$ and related estimates
Pascal Auscher
This article focuses on estimates for objects associated to elliptic operators in divergence form: its semigroup, the gradient of the semigroup, functional calculus, square f…
Riesz transform on manifolds and Poincaré inequalities
Pascal Auscher, Thierry Coulhon
We study the validity of the inequality for the Riesz transform when and of its reverse inequality when on complete Riemannian manifolds under the doubling proper…
Riesz transform on manifolds and heat kernel regularity
Pascal Auscher, Thierry Coulhon, Xuan Thinh Duong +1
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…
Hardy spaces and divergence operators on strongly Lipschitz domains in
P. Auscher, E. Russ
Let be a strongly Lipschitz domain of $\reel^n$. Consider an elliptic second order divergence operator (including a boundary condition on ) and define a Hardy sp…
Lectures on the Kato square root problem
P. Auscher
This is the text of a series of three lectures given at the CMA of the Australian National University on the recent solution of the square root problem for divergence form elliptic…
Carleson measures, trees, extrapolation, and theorems
Pascal Auscher, Steve Hofmann, Camil Muscalu +2
The theory of Carleson measures, stopping time arguments, and atomic decompositions has been well-established in harmonic analysis. More recent is the theory of phase space analysi…