Boundary Value Problems
Volume 2008 (2008), Article ID 425256, 16 pages
doi:10.1155/2008/425256
Hermitean Cauchy integral decomposition of continuous functions on hypersurfaces
Ricardo Abreu Blaya1
, Juan Bory Reyes2
, Fred Brackx3
, Bram De Knock3
, Hennie De Schepper3
, Dixan Peña Peña6
and Frank Sommen6
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
6Department of Mathematical Analysis, Faculty of Sciences, Ghent University, Galglaan 2, 9000 Ghent, Belgium
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.