Asymptotic Behavior for a Class of Modified α-Potentials in a Half Space. (8th July 2010)

• Record Type: Journal Article
• Authors: Qiao, Lei; Deng, Guantie
• Other Names: Ding Shusen Academic Editor.
• Is Part Of: Journal of inequalities and applications. Volume 2010(2010)
• Publication Date: 2010-07-08
• Subjects: Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/2010/647627
• Languages: English
• ISSNs: 1029-242X

Abstract

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.