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

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7 papers · 1 filter

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…

math.CA2013

Homogeneous kernerls and self similar sets

Vasilis Chousionis, Mariusz Urbański

We consider singular integrals associated to homogeneous kernels on self similar sets. Using ideas from ergodic theory we prove, among other things, that in Euclidean spaces the pr…

math.CA2013

A note on weak convergence of singular integrals in metric spaces

Vasilis Chousionis, Mariusz Urbański

We prove that in any metric space $(X, d)$ the singular integral operators {equation*} T^k_{μ,\ve}(f)(x)=\int_{X\setminus B(x,\varepsilon)}k(x,y)f(y)dμ(y).{equation*} converge weakl…

math.CA2013

Strong and weak type estimates for singular integrals with respect to measures separated by AD-regular boundaries

Vasilis Chousionis, Xavier Tolsa

We prove weak and strong boundedness estimates for singular integrals in $R^{d}$ with respect to $(d - 1)$ -dimensional measures separated by Ahlfors-David regular boundaries, generali…

math.CA2011

Capacities associated with Calderón-Zygmund kernels

Vasilis Chousionis, Joan Mateu, Laura Prat +1

Analytic capacity is associated with the Cauchy kernel $1/ z$ and the $L^{\infty}$ -norm. For $n \in N$ , one has likewise capacities related to the kernels $K_i(x)=x_i^{2n-1}/|x…