Homogeneous kernerls and self similar sets
Classical Analysis and ODEs
2016-10-17 v1 Dynamical Systems
Abstract
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 principal values of singular integrals associated to real analytic, homogeneous kernels fail to exist a.e. on self similar sets satisfying some separation conditions. Furthermore in general metric groups, using similar techniques, we generalize a criterion of -unboundedness for singular integrals on self similar sets.
Cite
@article{arxiv.1309.6242,
title = {Homogeneous kernerls and self similar sets},
author = {Vasilis Chousionis and Mariusz Urbański},
journal= {arXiv preprint arXiv:1309.6242},
year = {2016}
}