Abreu-Blaya, Ricardo; Bory-Reyes, Juan; Delanghe, Richard; Sommen, Frank Harmonic multivector fields and the Cauchy integral decomposition in Clifford analysis. (English) Zbl 1063.30045 Bull. Belg. Math. Soc. - Simon Stevin 11, No. 1, 95-110 (2004). The authors deal with the problem to decompose a Hölder continuous \(k\)-grade multivector field \(F_k\) on the boundary \(\Gamma\) of a bounded open set \(\Omega \subset \mathbb{R}^n\) into a sum \(F_k = F_k^+ + F_k^-\) of harmonic \(k\)-grade multivector fields in \(\Omega^+ = \Omega\) and \(\Omega^- = \mathbb{R}^n \setminus (\Omega \cup \Gamma)\) respectively.This is equivalent to the analogue problem for harmonic forms dealt with by E. Dyn’kin [Complex Variables, Theory Appl. 31, 165–176 (1996; Zbl 0865.30056); J. Anal. Math. 73, 165–186 (1997; Zbl 0899.58001)]. Conditions for the field \(F_k\) are given, example giving its Cauchy transform has to be both left and right monogenic in \(\mathbb{R}^n \setminus \Gamma\). Reviewer: Klaus Habetha (Aachen) Cited in 2 ReviewsCited in 5 Documents MSC: 30G35 Functions of hypercomplex variables and generalized variables 31B10 Integral representations, integral operators, integral equations methods in higher dimensions 31B20 Boundary value and inverse problems for harmonic functions in higher dimensions 31B25 Boundary behavior of harmonic functions in higher dimensions Keywords:harmonic vector fields; Clifford analysis; Cauchy integral decomposition Citations:Zbl 0865.30056; Zbl 0899.58001 PDFBibTeX XMLCite \textit{R. Abreu-Blaya} et al., Bull. Belg. Math. Soc. - Simon Stevin 11, No. 1, 95--110 (2004; Zbl 1063.30045)