In this paper we study the problem of decomposing a Hölder
continuous $k$-grade
multivector field $F_{k}$ on the boundary $\Gamma$ of an open bounded subset
$\Omega$
in Euclidean space $\R^{n}$ into a sum $F_{k}=F_{k}^{+}+F_{k}^{-}$ of harmonic
$k$-grade multivector fields $F_{k}^{\pm}$ in $\Omega_{+}=\Omega$ and
$\Omega_{-}=\R^{n}\setminus (\Omega\cup\Gamma)$ respectively.
The necessary and sufficient conditions upon $F_{k}$ we thus obtain
complement those proved by Dyn'kin in [20,21] in the case where $F_{k}$ is a
continuous $k$-form on $\Gamma$. Being obtained within the framework of Clifford
analysis and hence being of a pure function theoretic nature, they once more
illustrate
the importance of the interplay between Clifford analysis and classical real
harmonic analysis.
@article{1080056163,
author = {Abreu-Blaya, Ricardo and Bory-Reyes, Juan and Delanghe, Richard and Sommen, Frank},
title = {Harmonic multivector fields and the Cauchy integral decomposition in
Clifford analysis},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {11},
number = {1},
year = {2004},
pages = { 95-110},
language = {en},
url = {http://dml.mathdoc.fr/item/1080056163}
}
Abreu-Blaya, Ricardo; Bory-Reyes, Juan; Delanghe, Richard; Sommen, Frank. Harmonic multivector fields and the Cauchy integral decomposition in
Clifford analysis. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2004) no. 1, pp. 95-110. http://gdmltest.u-ga.fr/item/1080056163/