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Complex Analysis and Operator Theory

, Volume 7, Issue 3, pp 673–693 | Cite as

Riemann Boundary Value Problems for Iterated Dirac Operator on the Ball in Clifford Analysis

  • Min KuEmail author
  • Yingxiong Fu
  • Kähler Uwe
  • Cerejeiras Paula
Article

Abstract

In this paper we consider the Riemann boundary value problem for null solutions to the iterated Dirac operator over the ball in Clifford analysis with boundary data given in \(\mathbb L _{p}\left(1<p<+\infty \right)\)-space. We will use two different ways to derive its solution, one which is based on the Almansi-type decomposition theorem for null solutions to the iterated Dirac operator and a second one based on the poly-Cauchy type integral operator.

Keywords

Clifford analysis Riemann boundary value problem  Iterated Dirac operator 

Mathematics Subject Classification (2000)

30D10 30G35 32A25 58A10 

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Copyright information

© Springer Basel 2012

Authors and Affiliations

  • Min Ku
    • 1
    Email author
  • Yingxiong Fu
    • 1
    • 2
  • Kähler Uwe
    • 1
  • Cerejeiras Paula
    • 1
  1. 1.Department of Mathematics, Center for Research and Development in Mathematics and ApplicationsUniversity of Aveiro AveiroPortugal
  2. 2.Faculty of Mathematics and Computer ScienceHubei UniversityHubeiChina

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