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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…