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

Singular integrals on self-similar sets and removability for Lipschitz harmonic functions in Heisenberg groups