Criteria for monogenicity of Clifford algebra-valued functions on fractal domains
It is assumed a compact domain \(G\subset\mathbb{R}^{n+1}\) with a fractal boundary \(\Gamma\). The authors consider a \(\text{Cl}_{0,n}\)-valued function \(U\) on \(\overline G\), which is harmonic in \(G\) and Hölder-continuous on \(\Gamma\). By using the box dimension of the boundary for Hölder-continuous \(\text{Cl}_{0,n}\)-valued functions a Clifford-Cauchy transform can be defined. This is done by the authors in former papers. Necessary and sufficient conditions for the monogenicity of \(U\) in terms of the values of the fractal boundary is given. This result generalizes a corresponding one obtained by the first author for Ahlfors-David boundaries.
scientific article; zbMATH DE number 5797836
scientific article