In this paper the Theodoresco transform is used to show that, under additional assumptions, each Holder continuous function f defined on the boundary Γ of a fractal domain Ω ⊂ ℝ2n can be expressed as f = Ψ+ − Ψ−, where Ψ± are Holder continuous functions on Γ and Hermitian monogenically extendable to Ω and to ℝ2n ∖ (Ω ∪ Γ) respectively.