44 citations · 171 across the 20 of their papers we have counts for
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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…
A note on weak convergence of singular integrals in metric spaces
Vasilis Chousionis, Mariusz Urbański
We prove that in any metric space 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…
Diophantine approximation in Banach spaces
Lior Fishman, David S. Simmons, Mariusz Urbański
In this paper, we extend the theory of simultaneous Diophantine approximation to infinite dimensions. Moreover, we discuss Dirichlet-type theorems in a very general framework and d…
Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces
Lior Fishman, David S. Simmons, Mariusz Urbański
In this paper, we provide a complete theory of Diophantine approximation in the limit set of a group acting on a Gromov hyperbolic metric space. This summarizes and completes a lon…