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.
A class of -potentials represented as the sum of modified Green potential and
modified Poisson integral are proved to have the growth estimates at infinity in the upper-half space of the -dimensional Euclidean space, where the function is a positive non-decreasing function on the
satisfying certain conditions. This result generalizes the growth properties of analytic functions, harmonic functions, and superharmonic functions.