Nonlinear potential analysis in Morrey spaces on Carnot groups |
Received:November 01, 2023 Revised:December 24, 2023 |
Key Words:
Riesz potential, Bessel potential, Wolff potential, Morrey space, Carnot group
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Fund Project:Natural Science Foundation of Ningxia (Grant No.\ 2023AAC03001) and Natural Science Foundation of China(Grant No.\ 12261068) |
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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 abstractharmonic 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. |
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