Journal of Operator Theory

Volume 39, Issue 2, Spring 1998 pp. 297-308.

A decomposition theorem in Clifford analysis

Authors: John Ryan
Author institution: Department of Mathematics, University of Arkansas, Fayetteville, AR 72701, U.S.A.

Summary: A modified Cauchy integral formula is used to show that each monogenic function $f$ defined on a sector domain and satisfying $\| f(x)\|\leq C\| x\|^{-n+1}$ can be expressed as $f=f_{1}+f_{2}$. Here $f_{1}$ is monogenic on the sector domain and monogenically extends to upper half space, while $f_{2}$ monogenically extends to lower half space. Moreover, $\| f_{j}(x)\|\leq C\|x\|^{-n+1}$ on these extended domains, for $j=1$ or $2$. Similar decompositions are obtained over more general unbounded domains, and for more general types of monogenic functions.

Keywords: Cauchy kernels, monogenic functions

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