Criteria for monogenicity of Clifford algebra-valued functions on fractal domains

Suppose that Omega is a bounded domain with fractal boundary Gamma in R(n+1) and let R(0,n) be the real Clifford algebra constructed over the quadratic space R(n). Furthermore, let U be a R(0,n)-valued function harmonic in Omega and Holder-continuous up to Gamma. By using a new Clifford Cauchy transform for Jordan domains in R(n+1) with fractal boundaries, we give necessary and sufficient conditions for the monogenicity of U in terms of its boundary value u = U|(Gamma). As a consequence, the results of Abreu Blaya et al. (Proceedings of the 6th International ISAAC Congress Ankara, 167-174, World Scientific) are extended, which require Gamma to be Ahlfors-David regular.