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

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

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-dimensiona...

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Main Authors: Lei Qiao, Guantie Deng
Format: Article
Language:English
Published: SpringerOpen 2010-01-01
Series:Journal of Inequalities and Applications
Online Access:http://dx.doi.org/10.1155/2010/647627
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spelling doaj-df6a38644f394b7ea8577997393970212020-11-25T00:24:17ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2010-01-01201010.1155/2010/647627Asymptotic Behavior for a Class of Modified α-Potentials in a Half SpaceLei QiaoGuantie DengA 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. http://dx.doi.org/10.1155/2010/647627
collection DOAJ
language English
format Article
sources DOAJ
author Lei Qiao
Guantie Deng
spellingShingle Lei Qiao
Guantie Deng
Asymptotic Behavior for a Class of Modified α-Potentials in a Half Space
Journal of Inequalities and Applications
author_facet Lei Qiao
Guantie Deng
author_sort Lei Qiao
title Asymptotic Behavior for a Class of Modified α-Potentials in a Half Space
title_short Asymptotic Behavior for a Class of Modified α-Potentials in a Half Space
title_full Asymptotic Behavior for a Class of Modified α-Potentials in a Half Space
title_fullStr Asymptotic Behavior for a Class of Modified α-Potentials in a Half Space
title_full_unstemmed Asymptotic Behavior for a Class of Modified α-Potentials in a Half Space
title_sort asymptotic behavior for a class of modified α-potentials in a half space
publisher SpringerOpen
series Journal of Inequalities and Applications
issn 1025-5834
1029-242X
publishDate 2010-01-01
description 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.
url http://dx.doi.org/10.1155/2010/647627
work_keys_str_mv AT leiqiao asymptoticbehaviorforaclassofmodifiedx03b1potentialsinahalfspace
AT guantiedeng asymptoticbehaviorforaclassofmodifiedx03b1potentialsinahalfspace
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