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| 摘要: |
| 本文研究了关于Heisenberg群上的广义Morrey空间和Carnot群上的Lebesgue空间中Riesz位势算子或者分数阶极大算子的行为.根据Heisenberg群中抽象调和分析方法以及subLaplacian算子的Dirichlet问题解的表示公式，本文主要给出了关于齐次Carnot群G上消失的广义Morrey空间VLp，ψ（G）中的加权Hardy算子、分数阶极大算子和分数阶位势算子的有界性刻画.进而也得到无消失模的广义Morrey空间上Morrey位势的浸入不等式.所有这些结果推广了关于Heisenberg群上的广义Morrey空间和Carnot群上的Lebesgue空间中的相关结论. |
| 关键词: Carnot群 加权Hardy算子 分数阶极大算子 分数阶位势算子 广义Morrey空间 |
| DOI： |
| 分类号:O174.2;O177.5;O152.8 |
| 基金项目:Supported by Natural Science Foundations of China (11261041; 11271045; 11461053); Natural Science Foundations of Ningxia (NZ15055); Research Starting Funds for Imported Talents of Ningxia University. |
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| SOME PROPERTIES IN THE GENERALIZED MORREY SPACES ON HOMOGENOUS CARNOT GROUPS |
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LONG Pin-hong,HAN Hui-li
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| Abstract: |
| In this paper, the behaviors for the Riesz potential or fractional maximal operator in the generalized Morrey spaces on the Heisenberg group and the Lebesgue spaces on the Carnot group are studied. According to the methods of abstract harmonic analysis in Heisenberg group and the representation formula of solution of Dirichlet problem for subLaplacian, we mainly give some characterizations for the boundedness of the weighted Hardy operator, fractional maximal operator and fractional potential operator in the vanishing generalized Morrey space VLp,ψ(G) on homogenous Carnot group G. Moreover, we also obtain the embedding inequality for Morrey potentials in such these spaces without vanishing norm. All these results above generalize the related ones in the generalized Morrey spaces on the Heisenberg group and the Lebesgue spaces on the Carnot group. |
| Key words: Carnot group weighted Hardy operator fractional maximal operator potential operator generalized Morrey space |
