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).
Author NameAffiliation
Pinhong LONG School of Mathematics and Statistics, Ningxia University, Ningxia 750021, P. R. China 
Huili HAN School of Mathematics and Computer Science, Ningxia Normal University, Ningxia 756000, P. R. China 
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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
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