Homogeneous kernels and self similar sets Vasilis ChousionisMariusz Urbanski 32A5530L99Singular integralsself similar setsreal analyticitymetric spaces We consider singular integrals associated with 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 with real analytic, homogeneous kernels fail to exist almost everywhere on self-similar sets satisfying some separation conditions. Furthermore, in general metric groups, using similar techniques, we generalize a criterion of $L^2$-unboundedness for singular integrals on self-similar sets. Indiana University Mathematics Journal 2015 text pdf 10.1512/iumj.2015.64.5491 10.1512/iumj.2015.64.5491 en Indiana Univ. Math. J. 64 (2015) 411 - 431 state-of-the-art mathematics http://iumj.org/access/