Vasilis Chousionis

Singular integrals on Sierpinski gaskets

We construct a class of singular integral operators associated with homogeneous Calderon-Zygmund standard kernels on d-dimensional, d < 1, Sierpinski gaskets Ed. These operators are bounded in L2(μd) and their principal values diverge μd almost everywhere, where μd is the natural (d-dimensional) measure on Ed.

Boundedness and convergence for singular integrals of measures separated by Lipschitz graphs

We shall consider the truncated singular integral operators T_{\mu, K}^{\epsilon}f(x)=\int_{\mathbb{R}^{n}\setminus B(x,\epsilon)}K(x-y)f(y)d\mu y and related maximal operators

Singular Integrals on Self-similar Subsets of Metric Groups

T_{\mu,K}^{\ast}f(x)=\underset{\epsilon >0}{\sup}| T_{\mu,K}^{\epsilon}f(x)|

Calderón–Zygmund kernels and rectifiability in the plane☆

. We shall prove for a large class of kernels

DIRECTED POROSITY ON CONFORMAL ITERATED FUNCTION SYSTEMS AND WEAK CONVERGENCE OF SINGULAR INTEGRALS

K

Singular integrals on self-similar sets and removability for Lipschitz harmonic functions in Heisenberg groups

and measures

Singular Integrals on Ahlfors-David Regular Subsets of the Heisenberg Group

\mu

Fractal solutions of linear and nonlinear dispersive partial differential equations

and

Conformal graph directed Markov systems on Carnot groups

\nu

Removable sets for Lipschitz harmonic functions on Carnot groups

that if