8 citations · 8 across the 11 of their papers we have counts for
16 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+1}…
The dimension spectrum of the infinitely generated Apollonian gasket
Vasileios Chousionis, Dmitriy Leykekhman, Mariusz Urbański +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…
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 cancella…
Rigorous Hausdorff dimension estimates for conformal fractals
Vasileios Chousionis, Dmitriy Leykekhman, Mariusz Urbański +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 strong geometric lemma in the Heisenberg group
Vasileios Chousionis, Sean Li, Robert Young
We prove that in the first Heisenberg group, unlike Euclidean spaces and higher dimensional Heisenberg groups, the best possible exponent for the strong geometric lemma for intrins…
The Riesz tranform on intrinsic Lipschitz graphs in the Heisenberg group
Vasileios Chousionis, Sean Li, Robert Young
We prove that the Heisenberg Riesz transform is --unbounded on a family of intrinsic Lipschitz graphs in the first Heisenberg group . We construct this family by c…
The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups
Vasileios Chousionis, Sean Li, Robert Young
We show that the --numbers of intrinsic Lipschitz graphs of Heisenberg groups are locally Carleson integrable when . Our technique relies on a recent Do…
Singular integrals on regular curves in Carnot groups
Vasileios Chousionis, Sean Li, Scott Zimmerman
Let be any Carnot group. We prove that if a convolution type singular integral associated with a -dimensional Calderón-Zygmund kernel is -bounded on horizontal…
Porosity in conformal dynamical systems
Vasileios Chousionis, Mariusz Urbański
In this paper we study various aspects of porosities for conformal fractals. We first explore porosity in the general context of infinite graph directed Markov systems (GDMS), and…
Bi-Lipschitz embeddings of Heisenberg submanifolds into Euclidean spaces
Vasileios Chousionis, Sean Li, Vyron Vellis +1
The Heisenberg group equipped with a sub-Riemannian metric is one of the most well known examples of a doubling metric space which does not admit a bi-Lipschitz embedd…
On the dimension spectrum of infinite subsystems of continued fractions
Vasileios Chousionis, Dmitriy Leykekhman, Mariusz Urbański
In this paper we study the dimension spectrum of continued fractions with coefficients restricted to infinite subsets of natural numbers. We prove that if is any arithmetic pro…
The dimension spectrum of graph directed Markov systems
Vasileios Chousionis, Dmitriy Leykekhman, Mariusz Urbański
In this paper we study the dimension spectrum of general conformal graph directed Markov systems modeled by countable state symbolic subshifts of finite type. We perform a comprehe…
Boundedness of singular integrals on intrinsic graphs in the Heisenberg group
Vasileios Chousionis, Katrin Fässler, Tuomas Orponen
We study singular integral operators induced by -dimensional Calderón-Zygmund kernels in the Heisenberg group. We show that if such an operator is bounded on vertical pl…
Nonnegative kernels and -rectifiability in the Heisenberg group
Vasileios Chousionis, Sean Li
Let be an -Ahlfors regular subset of the Heisenberg group . We prove that there exists a -homogeneous kernel such that if is contained in a -reg…
Intrinsic Lipschitz graphs and vertical -numbers in the Heisenberg group
Vasileios Chousionis, Katrin Fässler, Tuomas Orponen
The purpose of this paper is to introduce and study some basic concepts of quantitative rectifiability in the first Heisenberg group . In particular, we aim to demonstr…
Square functions of fractional homogeneity and Wolff potentials
Vasileios Chousionis, Laura Prat, Xavier Tolsa
In this paper it is shown that for anymeasure in and for a non-integer , the Wolff energy $\displaystyle{\iint_0^\infty(\frac{μ(B(x,r))}{r^s})^2\,\frac{dr…