Nonlinear Potential Analysis in Morrey Spaces on Carnot Groups

作     者：Pinhong LONG Huili HAN 

作者机构：School of Mathematics and StatisticsNingxia University School of Mathematics and Computer ScienceNingxia Normal University 

出 版 物：《Journal of Mathematical Research with Applications》 (数学研究及应用(英文))

年 卷 期：2024年第5期

页      面：669-680页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the Natural Science Foundation of Ningxia (Grant No. 2023AAC03001) the National Natural Science Foundation of China (Grant No. 12261068) 

摘      要：In this paper, the nonlinear potential theory in the Morrey spaces on Euclidean spaces and the Lebesgue spaces on the Carnot group are studied. According to the methods of abstract harmonic analysis in Heisenberg group and abstract potential theory in carnot group, we mainly give some characterizations for Riesz, Bessel and Wolff potentials, and the corresponding capacities in the Morrey spaces on Carnot group. Meanwhile, we also interpret the relation among Riesz and Bessel type capacities and Housdorff content in the Morrey spaces on Carnot group. All these results above generalize the related ones in the Morrey spaces on Euclidean spaces and the Lebesgue spaces on the Carnot group.