A sharp Trudinger type inequality for harmonic functions and its applications

作者：Tan, Yili; An, Yongli; Wang, Hong; Liu, Jing^*

来源：JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017, 2017(1): 250.

DOI：10.1186/s13660-017-1522-9

• Trudinger type inequality
• Cauchy-Riesz kernel function
• modified Poisson type kernel
• Morrey representation

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.

• 出版日期2017-10-6
• 单位中国科学技术大学