Hermitean Téodorescu Transform Decomposition of Continuous Matrix Functions on Fractal Hypersurfaces
1 Facultad de Informática y Matemática, Universidad de Holguín, Holguín 80100, Cuba
2 Departamento de Matemática, Universidad de Oriente, Santiago de Cuba 90500, Cuba
3 Clifford Research Group, Department of Mathematical Analysis, Faculty of Engineering, Ghent University, Galglaan 2, 9000 Gent, Belgium
Boundary Value Problems 2010, 2010:791358 doi:10.1155/2010/791358Published: 20 May 2010
We consider Hölder continuous circulant () matrix functions defined on the fractal boundary of a domain in . The main goal is to study under which conditions such a function can be decomposed as , where the components are extendable to -monogenic functions in the interior and the exterior of , respectively. -monogenicity are a concept from the framework of Hermitean Clifford analysis, a higher-dimensional function theory centered around the simultaneous null solutions of two first-order vector-valued differential operators, called Hermitean Dirac operators. -monogenic functions then are the null solutions of a () matrix Dirac operator, having these Hermitean Dirac operators as its entries; such matrix functions play an important role in the function theoretic development of Hermitean Clifford analysis. In the present paper a matricial Hermitean Téodorescu transform is the key to solve the problem under consideration. The obtained results are then shown to include the ones where domains with an Ahlfors-David regular boundary were considered.