8 citations · 8 across the 11 of their papers we have counts for
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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}…
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…
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…
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…