| 加权Baouendi-Grushin型算子的基本解与一类加权Hardy不等式(英文) |
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| 引用本文： | 狄艳媚,金永阳,沈守枫,姜丽亚. 加权Baouendi-Grushin型算子的基本解与一类加权Hardy不等式(英文)[J]. 数学季刊, 2012, 0(2): 274-279 |
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| 作者姓名： | 狄艳媚 金永阳 沈守枫 姜丽亚 |
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| 作者单位： | Department of Applied Mathematics,Zhejiang University of Technology |
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| 基金项目： | Supported by the Natural Science Foundation of Zhejiang Province(Y6090359,Y6090383);Supported by the Department of Education of Zhejiang Province(Z200803357) |
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| 摘 要： | In this paper we obtain the fundamental solution for a class of weighted BaouendiGrushin type operator Lp,γ,αu = ▽γ·(|▽γu|p-2ρα▽γu) on Rm+n with singularity at the origin,where ▽γ is the gradient operator defined by ▽γ =（▽x,|x|γ▽y） and ρ is the distance function.As an application,we get some Hardy type inequalities associated with ▽γ.
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| 关 键 词： | fundamental solution weighted Baouendi-Grushin type operator Hardy type inequality |
Fundamental Solution for Weighted Baouendi-Grushin Type Operators and a Class of Weighted Hardy Inequality |
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| DI Yan-mei,JIN Yong-yang,SHEN Shou-feng,JIANG Li-ya. Fundamental Solution for Weighted Baouendi-Grushin Type Operators and a Class of Weighted Hardy Inequality[J]. Chinese Quarterly Journal of Mathematics, 2012, 0(2): 274-279 |
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| Authors: | DI Yan-mei JIN Yong-yang SHEN Shou-feng JIANG Li-ya |
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| Affiliation: | (Department of Applied Mathematics,Zhejiang University of Technology,Hangzhou 310032,China) |
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| Abstract: | In this paper we obtain the fundamental solution for a class of weighted BaouendiGrushin type operator Lp,γ,αu = ▽γ ·(|▽γu|p-2ρα▽γu) on Rm+n with singularity at the origin,where ▽γ is the gradient operator defined by ▽γ =（▽x,|x|γ▽y） and ρ is the distance function.As an application,we get some Hardy type inequalities associated with ▽γ. |
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| Keywords: | fundamental solution weighted Baouendi-Grushin type operator Hardy type inequality |
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