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Clifford analysis may be regarded as a direct and elegant generalization to higher dimensions of the theory of holomorphic functions in the complex plane, centred around the notion of monogenic function, i.e. a null solution of the Dirac operator. This paper dealswith axial and biaxialmonogenic functions containing sphericalmonogenics. They are constructed bymeans of two fundamentalmethods of Clifford analysis, namely the Cauchy-Kowalevski extension and monogenic plane waves. [ABSTRACT FROM AUTHOR]

Let Ω ⊂ ℝ be a Jordan domain with d-summable boundary Γ. The main gol of this paper is to estimate the Hölder norm of a fractal version of the Hilbert transform in the Clifford analysis context acting from Hölder spaces of Clifford algebra valued functions defined on Γ. The explicit expression for the upper bound of the norm provided here is given in terms of the Hölder exponents, the diameter of Γ and certain d-sum ( d > d) of the Whitney decomposition of Ω. The result obtained is applied to standard Hilbert transform for domains with left Ahlfors-David regular surface. [ABSTRACT FROM AUTHOR]

In this article we present a closed formula for the CK-extension of the Gaussian distribution in m, and the monogenic version of the holomorphic function [image omitted] which is a fundamental solution of the generalized Cauchy-Riemann operator. [ABSTRACT FROM AUTHOR]

In this article, half Robin problems for powers of Dirac operator in the unit ball B of Rm (m x≥ 3) are investigated. By using a certain kind of decomposition of k-monogenic functions an explicit formula for the solution and the necessary and sufficient conditions for the solvability of the problems are obtained. [ABSTRACT FROM AUTHOR]