Boundary Value Problems
Volume 2008 (2008), Article ID 425256, 16 pages
doi:10.1155/2008/425256
Research Article

Hermitean Cauchy Integral Decomposition of Continuous Functions on Hypersurfaces

Ricardo Abreu Blaya,1 Juan Bory Reyes,2 Fred Brackx,3 Bram De Knock,3 Hennie De Schepper,3 Dixan Peña Peña,4 and Frank Sommen4

1Facultad de Informática y Matemática, Universidad de Holguín, Holguín 80100, Cuba
2Departamento de Matemática, Universidad de Oriente, Santiago de Cuba 90500, Cuba
3Department of Mathematical Analysis, Faculty of Engineering, Ghent University, Galglaan 2, 9000 Ghent, Belgium
4Department of Mathematical Analysis, Faculty of Sciences, Ghent University, Galglaan 2, 9000 Ghent, Belgium

Received 12 August 2008; Accepted 23 October 2008

Academic Editor: Colin Rogers

Copyright © 2008 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.

Abstract

We consider Hölder continuous circulant (2×2) matrix functions G21 defined on the Ahlfors-David regular boundary Γ of a domain Ω in ℝ2n. 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 two-sided H-monogenic functions in the interior and the exterior of Ω, respectively. H-monogenicity is 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 functions have been crucial for the development of function theoretic results in the Hermitean Clifford context.