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Abstract
In this article, we consider a class of Dirichlet problems with L p boundary data for polyharmonic functions in the unit disc. Using higher order Poisson kernels due to Begehr et al. [H. Begehr, J. Du, and Y. Wang, A Dirichlet problem for polyharmonic functions, Ann. Mat. Pura Appl. 187(4) (2008), pp. 435–457; Z. Du, G. Guo, and N. Wang, Decompositions of functions and Dirichlet problems in the unit disc, J. Math. Anal. Appl. 362(1) (2010), pp. 1–16], we give the integral representation solutions of the problems.
Acknowledgements
The first author is partially supported by the NNSF grants (Nos 10871150 and 11126065) and by (Macao) FDCT 056/2010/A3. He acknowledges support and help of Professors Drs Jinyuan Du, Heinrich Begehr and Tao Qian. All the authors greatly appreciate the referees for their careful reading of the paper, helpful questions and enlightening suggestions, which have improved the quality of this article.