  In this paper we study singular integrals on small (that is, measure zero and
lower than full dimensional) subsets of metric groups. The main examples of the
groups we have in mind are Euclidean spaces and Heisenberg groups. In addition
to obtaining results in a very general setting, the purpose of this work is
twofold; we shall extend some results in Euclidean spaces to more general
kernels than previously considered, and we shall obtain in Heisenberg groups
some applications to harmonic (in the Heisenberg sense) functions of some
results known earlier in Euclidean spaces.
