TITLE:
Lp Polyharmonic Dirichlet Problems in the Upper Half Plane
AUTHORS:
Kanda Pan
KEYWORDS:
Dirichlet Problem, Polyharmonic Function, Higher Order Poisson Kernels, Higher Order Pompeiu Operators, Non-Tangential Maximal Function, Uniqueness
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.5 No.14,
December
11,
2015
ABSTRACT: In this article, a class of Dirichlet problem with Lp 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.