V. Chousionis

activity

20082018

most citedFractal solutions of linear and nonlinear dispersive partial differential equations

28 citations · 60 across the 15 of their papers we have counts for

collaborators

Showing 2014Show all

4 papers · 1 filter

math.MG2014★ 3 cited

Marstrand's density theorem in the Heisenberg group

Vasilis Chousionis, Jeremy T. Tyson

We prove that if $μ$ is a Radon measure on the Heisenberg group $H^{n}$ such that the density $Θ^{s} (μ, \cdot)$ , computed with respect to the Korányi metric $d_{H}$ , exists and i…

math.AP2014★ 28 cited

Fractal solutions of linear and nonlinear dispersive partial differential equations

V. Chousionis, M. Burak Erdoğan, Nikolaos Tzirakis

In this paper we study fractal solutions of linear and nonlinear dispersive PDE on the torus. In the first part we answer some open questions on the fractal solutions of linear Sch…

math.CA2014

Some Calderón-Zygmund kernels and their relations to Wolff capacities and rectifiability

Vasilis Chousionis, Laura Prat

We consider the Calderón-Zygmund kernels $K_{α, n} (x) = (x_{i}^{2 n - 1} /∣ x ∣^{2 n - 1 + α})_{i = 1}^{d}$ in $R^{n}$ for $0 < α \leq 1$ and $n \in N$ . We show that, on the plane, for $0<…

math.CA2014★ 2 cited

Square functions and uniform rectifiability

Vasilis Chousionis, John Garnett, Triet Le +1

In this paper it is shown that an Ahlfors-David $n$ -dimensional measure $μ$ on $R^{d}$ is uniformly $n$ -rectifiable if and only if for any ball $B (x_{0}, R)$ centered at $\oper…