Computational Methods and Function Theory 2 (2002), No. 1, 215--228
Copyright Heldermann Verlag 2002
Dejenie A. Lakew
lakew_d@uapd.edu, Department of Mathematical Sciences and Technology, University of Arkansas at Pine Bluff, 1200 N University Drive M/S 4989, Pine Bluff, Arkansas 71601, U.S.A.
John Ryan
jryan@uark.edu, Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701, U.S.A.
For $\Omega$ a sufficiently smooth unbounded domain in $\mathbb{R}^n$ we develop a decomposition result for the Sobolev space $W_{\Cl_{0,n}}^{pl-1} (\Omega)$. We also use modified Cauchy-Green type kernels to construct Clifford analytic-complete function systems in the generalized Bergman space $B^{p,l}_{\Cl_{0,n}}(\Omega):=\ker D^{l}(\Omega)\cap W_{\Cl_{0,n}}^{p,l-1} (\Omega)$, where $D^{l}$ is the $l$-th iterate of the Dirac operator, $l$ is a positive integer less than $n$ and $n/(n-l+1)
Keywords: Clifford Analysis, complete function systems, Bergman spaces, decomposition spaces, elliptic boundary value problems, Dirac operators and hyperbolas.
MSC 2000: 30G35, 35C15, 35F15, 35J05, 30E20, 35A35.
[FullText-pdf (248 K)] [FullText-ps (316 K)]