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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Center for Research and Development in Mathematics and Applications, University of Aveiro, 3810-193,  Aveiro, Portugal

    Min Ku, Yingxiong Fu, Kähler Uwe & Cerejeiras Paula

  2. Faculty of Mathematics and Computer Science, Hubei University, Hubei, China

    Yingxiong Fu

Authors
  1. Min Ku
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  2. Yingxiong Fu
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  3. Kähler Uwe
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  4. Cerejeiras Paula
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Corresponding author

Correspondence to Min Ku.

Additional information

Communicated by Irene Sabadini.

This work was supported by FEDER funds through COMPETE–Operational Programme Factors of Competitiveness (“Programa Operacional Factores de Competitividade”), by Portuguese founds through the Center for Research and Development in Mathematics and Applications (University of Aveiro) and the Portuguese Foundation for Science and Technology (“FCT–Fundação para a Ciência e a Tecnologia”), within project PEst-C/MAT/UI4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690 and by NNSF of China under Grant No.61170032. The first author is the recipient of Postdoctoral Foundation from FCT (Portugal) under Grant No.SFRH/BPD/74581/2010 and from China under Grant No. 201003111.

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Ku, M., Fu, Y., Uwe, K. et al. Riemann Boundary Value Problems for Iterated Dirac Operator on the Ball in Clifford Analysis. Complex Anal. Oper. Theory 7, 673–693 (2013). https://doi.org/10.1007/s11785-012-0277-z

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  • DOI: https://doi.org/10.1007/s11785-012-0277-z

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