28 citations · 60 across the 15 of their papers we have counts for
5 papers · 1 filter
Removable sets for Lipschitz harmonic functions on Carnot groups
Vasilis Chousionis, Valentino Magnani, Jeremy T. Tyson
Let G be a Carnot group with homogeneous dimension Q larger than 2 and let L be a sub-Laplacian on G. We prove that the critical dimension for removable sets of Lipschitz L-harmoni…
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…
Removable sets for homogeneous linear PDE in Carnot groups
Vasilis Chousionis, Jeremy T. Tyson
Let $\cL$ be a homogeneous left invariant differential operator on a Carnot group. Assume that both $\cL$ and $\cL^t$ are hypoelliptic. We study the removable sets for $\cL$-soluti…
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…
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 with respect to -dimensional measures separated by Ahlfors-David regular boundaries, generali…