调和函数的一个尖锐的特鲁丁格型不等式及其应用。
A sharp Trudinger type inequality for harmonic functions and its applications.
作者信息
Tan Yili, An Yongli, Wang Hong, Liu Jing
机构信息
College of Science, North China University of Science and Technology, Tangshan, 063210 China.
College of Information Engineering, North China University of Science and Technology, Tangshan, 063210 China.
出版信息
J Inequal Appl. 2017;2017(1):250. doi: 10.1186/s13660-017-1522-9. Epub 2017 Oct 6.
The present paper introduces a sharp Trudinger type inequality for harmonic functions based on the Cauchy-Riesz kernel function, which includes modified Poisson type kernel in a half plane considered by Xu et al. (Bound. Value Probl. 2013:262, 2013). As applications, we not only obtain Morrey representations of continuous linear maps for harmonic functions in the set of all closed bounded convex nonempty subsets of any Banach space, but also deduce the representation for set-valued maps and for scalar-valued maps of Dunford-Schwartz.
本文基于柯西 - 里斯核函数介绍了一个关于调和函数的尖锐特鲁丁格型不等式，其中包括徐等人（《边值问题》2013:262，2013）所考虑的半平面中的修正泊松型核。作为应用，我们不仅在任意巴拿赫空间的所有闭有界凸非空子集的集合中得到了调和函数连续线性映射的莫雷表示，还推导了邓福德 - 施瓦茨集值映射和标量值映射的表示。
Zotero 插件