Hermitean Cauchy Integral Decomposition of Continuous Functions on Hypersurfaces

• Main Authors: Frank Sommen, Dixan Peña Peña, Hennie De Schepper, Bram De Knock, Fred Brackx, Juan Bory Reyes, Ricardo Abreu Blaya
• Format: Article
• Language: English
• Published: SpringerOpen 2008-12-01
• Series: Boundary Value Problems
• Online Access: http://dx.doi.org/10.1155/2008/425256

We consider Hölder continuous circulant (2×2) matrix functions G21 defined on the Ahlfors-David regular boundary Γ of a domain Ω in â„Â2n. 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.