加权Baouendi-Grushin型算子的基本解与一类加权Hardy不等式

数学季刊 ›› 2012, Vol. 27 ›› Issue (2): 274-279.

加权Baouendi-Grushin型算子的基本解与一类加权Hardy不等式

Department of Applied Mathematics, Zhejiang University of Technology

收稿日期:2011-10-14 出版日期:2012-06-30 发布日期:2023-03-30
作者简介:DI Yan-mei(1979-), female, native of Wenling, Zhejiang, a lecturer of Zhejiang University of Technology, M.S.D., engages in harmonic analysis.
基金资助:
Supported by the Natural Science Foundation of Zhejiang Province(Y6090359,Y6090383)； Supported by the Department of Education of Zhejiang Province(Z200803357)

Fundamental Solution for Weighted Baouendi-Grushin Type Operators and a Class of Weighted Hardy Inequality

Department of Applied Mathematics, Zhejiang University of Technology

Received:2011-10-14 Online:2012-06-30 Published:2023-03-30
About author:DI Yan-mei(1979-), female, native of Wenling, Zhejiang, a lecturer of Zhejiang University of Technology, M.S.D., engages in harmonic analysis.
Supported by:
Supported by the Natural Science Foundation of Zhejiang Province(Y6090359,Y6090383)； Supported by the Department of Education of Zhejiang Province(Z200803357)

摘要/Abstract

摘要： In this paper we obtain the fundamental solution for a class of weighted Baouendi-Grushin type operator L_p,γ,αu = ▽_γ·(|▽_γu|^p-2ρ^α▽_γu) on R^m+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.

关键词: fundamental solution, weighted Baouendi-Grushin type operator, Hardy type inequality

Abstract: In this paper we obtain the fundamental solution for a class of weighted Baouendi-Grushin type operator L_p,γ,αu = ▽_γ·(|▽_γu|^p-2ρ^α▽_γu) on R^m+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.

Key words: fundamental solution, weighted Baouendi-Grushin type operator, Hardy type inequality

中图分类号:

O178

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[J]. 数学季刊, 2012, 27(2): 274-279.

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, 27(2): 274-279.

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