  We investigate certain singular integral operators with Riesz-type kernels on
s-dimensional Ahlfors-David regular subsets of Heisenberg groups. We show that
$L^2$-boundedness, and even a little less, implies that $s$ must be an integer
and the set can be approximated at some arbitrary small scales by homogeneous
subgroups. It follows that the operators cannot be bounded on many self similar
fractal subsets of Heisenberg groups.
