Abstract
A modified Cauchy kernel is introduced over unbounded domains whose complement contains nonempty open sets. Basic results on Clifford analysis over bounded domains are now carried over to this more general context and to functions that are no longer assumed to be bounded. In particular Plemelj formulae are explicitly computed. Basic properties of the Cauchy transform over unbounded domains lying in a half space are investigated, and an orthogonal decomposition of theL2space for such a domain is set up. At the end a boundary value problem will be studied in the case of an unbounded domain without using weighted Sobolev spaces.
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