Boundary Value Problems
Volume 2010 (2010), Article ID 791358, 15 pages
Research Article

Hermitean Téodorescu Transform Decomposition of Continuous Matrix Functions on Fractal Hypersurfaces

1Facultad de Informática y Matemática, Universidad de Holguín, Holguín 80100, Cuba
2Departamento de Matemática, Universidad de Oriente, Santiago de Cuba 90500, Cuba
3Clifford Research Group, Department of Mathematical Analysis, Faculty of Engineering, Ghent University, Galglaan 2, 9000 Gent, Belgium

Received 18 December 2009; Accepted 12 April 2010

Academic Editor: Michel C. Chipot

Copyright © 2010 Ricardo Abreu-Blaya et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider Hölder continuous circulant (2×2) matrix functions G21 defined on the fractal boundary Γ of a domain Ω in 2n. The main goal is to study under which conditions such a function G21 can be decomposed as G21=G21+G21, where the components G21± are extendable to H-monogenic functions in the interior and the exterior of Ω, respectively. H-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. H-monogenic functions then are the null solutions of a (2×2) 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.