Nonlinear Potential Analysis in Morrey Spaces on Carnot Groups |
Received:November 04, 2023 Revised:April 08, 2024 |
Key Words:
Riesz potential Bessel potential Wolff potential Morrey space Carnot group
|
Fund Project:Supported by the Natural Science Foundation of Ningxia (Grant No.\,2023AAC03001) and the National Natural Science Foundation of China (Grant No.\,12261068). |
|
Hits: 183 |
Download times: 154 |
Abstract: |
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. |
Citation: |
DOI:10.3770/j.issn:2095-2651.2024.05.008 |
View Full Text View/Add Comment |