  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 $L^2$-unboundedness for
singular integrals on self similar sets.
