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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 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 with respect to -dimensional measures separated by Ahlfors-David regular boundaries, generali…