%0 Journal Article
%T <i>L<sup>p</sup></i> Polyharmonic Dirichlet Problems in the Upper Half Plane
%A Kanda Pan
%J Advances in Pure Mathematics
%P 828-834
%@ 2160-0384
%D 2015
%I Scientific Research Publishing
%R 10.4236/apm.2015.514077
%X In this article, a class of Dirichlet problem with <i>L<sup>p</sup></i> boundary data for poly-harmonic function in the upper half plane is mainly investigated. By introducing a sequence of kernel functions called higher order Poisson kernels and a hierarchy of integral operators called higher order Pompeiu operators, we obtain a main result on integral representation solution as well as the uniqueness of the polyharmonic Dirichlet problem under a certain estimate.
%K Dirichlet Problem
%K Polyharmonic Function
%K Higher Order Poisson Kernels
%K Higher Order Pompeiu Operators
%K Non-Tangential Maximal Function
%K Uniqueness
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=61843