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We consider Hölder continuous circulant (2 x 2) matrix functions Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. defined on the fractal boundary Γ of a domain Ω in ℝ2n. The main goal is to study under which conditions such a function Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. can be decomposed as Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed., where the components Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. 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 x 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. [ABSTRACT FROM AUTHOR]

Monogenic extension theorem of complex Clifford algebras-valued functions over a bounded domain with fractal boundary is obtained. The paper is dealing with the class of Hölder continuous functions. Applications to holomorphic functions theory of several complex variables as well as to that of the so-called biregular functions will be deduced directly from the isotonic approach. [ABSTRACT FROM AUTHOR]