We construct a class of singular integral operators associated with homogeneous Calderón-Zygmund standard kernels on $d$-dimensional, $d <1$, Sierpinski gaskets $E_d$. These operators are bounded in $L^2(\mu_d)$ and their principal values diverge $\mu_d$ almost everywhere, where $\mu_d$ is the natural ($d$-dimensional) measure on $E_d$.
V. Chousionis. "Singular integrals on Sierpinski gaskets." Publ. Mat. 53 (1) 245 - 256, 2009.