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Let [OMEGA] be a bounded open and oriented connected subset of [R.sup.n] which has a compact topological boundary [GAMMA], let C be the Dirac operator in [R.sup.n], and let [R.sub.0,n] be the Clifford algebra constructed over the quadratic space [R.sup.n]. An [R.sub.0,n]-valued smooth function f: [OMEGA] [right arrow] [R.sub.0,n] in [OMEGA] is called monogenic in [OMEGA] if Df = 0 in [OMEGA]. The aim of this paper is to present the most general condition on [GAMMA] obtained so far for which a Holder continuous function f can be decomposed as [F.sup.+] - [F.sup.-] = f on [GAMMA], where the components [F.sup.[+ or -]] are extendable to monogenic functions in [[OMEGA].sup.[+ or -]] with [[OMEGA].sup.+] := [OMEGA], and [[OMEGA].sup.-] := [R.sup.n]\([OMEGA] [union] [GAMMA]), respectively., CONTENTS 1. Introduction 2. Preliminaries. Clifford Algebras and Monogenic Functions 3. Approximate Dimension and d-Summability 4. The Jump Problem for Monogenic Functions References 1. Introduction The Clifford algebra is an [...]

We obtain some analogues of the Hilbert formulas on the unit circle for -hyperholomorphic function theory in for being a complex quaternionic number. The obtained formulas relate a pair of components of the boundary value of an -hyperholomorphic function in the unit disc with the other pair of components and, hence, being analogous to the case of the theory of functions of one complex variable. [ABSTRACT FROM AUTHOR]

Some boundary value problems are solved for time-harmonic electromagnetic fields on fractal domains, in the framework of exploiting hypercomplex function theory. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Let Γ be an n-dimensional rectifiable ∣F∣-regular surface in ℝn+1. Let u be a continuous ℝ0, n- valued function on Γ, where ℝ0, n is the Clifford algebra associated with ℝn. Then we prove that the weighted Cliffordian Cauchy transform (Multiple line equation(s) cannot be represented in ASCII text) has continuous limit values on F if and only if the truncated integrals (Multiple line equation(s) cannot be represented in ASCII text) converge uniformly in Γ as ϵ → 0. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to estimate the Hölder norm of a fractal version of the Hilbert transform in the Douglis analysis context acting from Hölder spaces of Douglis algebra valued functions defined on h -summable curves.