Asymptotic Behavior for a Class of Modified α-Potentials in a Half Space. (8th July 2010) - Qiao, Lei; Deng, Guantie
Abstract : A class ofα -potentials represented as the sum of modified Green potential and modified Poisson integral are proved to have the growth estimatesR α, l, l ( x ) = o ( x n β | x | l − 2 β + 2 h ( | x | ) − 1 ) at infinity in the upper-half space of then -dimensional Euclidean space, where the functionh ( | x | ) is a positive non-decreasing function on the interval( 0, ∞ ) satisfying certain conditions. This result generalizes the growth properties of analytic functions, harmonic functions, and superharmonic functions.