Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 647627, 14 pages
doi:10.1155/2010/647627
Research Article

Asymptotic Behavior for a Class of Modified α-Potentials in a Half Space

Lei Qiao1 and Guantie Deng2

1Department of Mathematics and Information Science, Henan University of Finance and Economics, Zhengzhou 450002, China
2Laboratory of Mathematics and Complex Systems, School of Mathematical Science, Beijing Normal University, MOE, Beijing 100875, China

Received 13 March 2010; Accepted 21 June 2010

Academic Editor: Shusen Ding

Copyright © 2010 Lei Qiao and Guantie Deng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A class of α-potentials represented as the sum of modified Green potential and modified Poisson integral are proved to have the growth estimates Rα,l,l(x)=o(xnβ|x|l−2β+2h(|x|)−1) at infinity in the upper-half space of the n-dimensional Euclidean space, where the function h(|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.