Let Γ be a geometrically finite or a quasi-Fuchsian Kleiman group such that ∞ ∈ Ω̊(v). We establish the relation X = clos _x L(1/1-a, a∈Ξ) for some countable sets Ξ ⊂ Ω(Γ) connected with actions of elements of Γ, and for the space X =C(Λ) or for the Hölder classes X = L^α(Λ), 0 < α < 1, where Λ = Λ(Γ) = ℂ\Ω is the limit set of Γ. Bibliography: 6 titles.