Cauchy transform and rectifiability in clifford analysis

Let Γ be an n-dimensional rectifiable Ahlfors-David regular surface in ℝⁿ⁺¹. Let u be a continuous ℝ_0,n-valued function on Γ, where ℝ_0,n is the Clifford algebra associated with ℝⁿ. Then we prove that the Cliffordian Cauchy transform (C_Γu)(x) := ∫_Γ y-x̄/A _n+1|y-x|ⁿ⁺¹n(y)u(y)dℋⁿ(y), x ∉ Γ, has continuous limit values on F if and only if the truncated integrals S_Γ,εu(z):= ∫ _{Γ\{|y-z|≤ε}} y-z̄/A_n+1|y-z| ⁿ⁺¹n(y)(u(y) - u(z))dℋⁿ(y) converge uniformly on Γ as ε → 0.