4 papers
On singular integrals with non-negative kernels in the Heisenberg group
Vasileios Chousionis, Sean Li, Lingxiao Zhang
In this paper we revisit nonnegative kernels in the first Heisenberg group $\He$, and in particular we further study the family $$K_α(x,y,z)= \frac{|z|^{α/2}}{\|(x,y,z)\|_{H}^{α…
Singular integrals on intrinsic graphs in step 2 Carnot groups
Vasileios Chousionis, Sean Li, Lingxiao Zhang
We study singular integral operators induced by Calderón-Zygmund kernels in any step- Carnot group . We show that if such an operator satisfies some natural cancell…
Rigorous Hausdorff dimension estimates for conformal fractals
Vasileios Chousionis, Dmitriy Leykekhman, Mariusz UrbaÅski +1
We develop a versatile framework which allows us to rigorously estimate the Hausdorff dimension of maximal conformal graph directed Markov systems in for .…
The dimension spectrum of the infinitely generated Apollonian gasket
Vasileios Chousionis, Dmitriy Leykekhman, Mariusz UrbaÅski +1
We prove that the infinitely generated Apollonian gasket has full Hausdorff dimension spectrum. Our proof, which is computer assisted, relies on an iterative technique introduced b…