Advances in Applied Clifford Algebras

, Volume 24, Issue 4, pp 1145–1157 | Cite as

Some Integral Representations and Singular Integral over Plane in Clifford Analysis



In this paper, Cauchy type integral and singular integral over hyper-complex plane \({\prod}\) are considered. By using a special Möbius transform, an equivalent relation between \({\widehat{H}^\mu}\) class functions over \({\prod}\) and \({H^\mu}\) class functions over the unit sphere is shown. For \({\widehat{H}^\mu}\) class functions over \({\prod}\) , we prove the existence of Cauchy type integral and singular integral over \({\prod}\) . Cauchy integral formulas as well as Poisson integral formulas for monogenic functions in upper-half and lower-half space are given respectively. By using Möbius transform again, the relation between the Cauchy type integrals and the singular integrals over \({\prod}\) and unit sphere is built.


Clifford algebra Möbius transform integral representation singular integral 


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© Springer Basel 2014

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanP.R. China

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