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We consider HÃƒÂ¶lder continuous circulant (2ÃƒÂ—2) matrix functions G21 defined on the Ahlfors-David regular boundary ÃŽÂ“ of a domain ÃŽÂ© in Ã¢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 G21Ã‚Â± are extendable to two-sided H-monogenic functions in the interior and the exterior of ÃŽÂ©, 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 (2ÃƒÂ—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

Hermitean Cauchy Integral Decomposition of Continuous Functions on Hypersurfaces