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

Abstract: A class of alpha-potentials represented as the sum of modified Green potential and modified Poisson integral are proved to have the growth estimates R-alpha,R-l,R-l(x) = o(x(n)(beta)|x|(l-2 beta+2)h(|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,infinity) satisfying certain conditions. This result generalizes the growth properties of analytic functions, harmonic functions, and superharmonic functions.
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