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

作　　者：DI Yan-mei JIN Yong-yang SHEN Shou-feng JIANG Li-ya 

机构地区：[1]Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310032, China

出　　处：《Chinese Quarterly Journal of Mathematics》2012年第2期274-279,共6页数学季刊（英文版）

基　　金：Foundation item： Supported by the Natural Science Foundation of Zhejiang Province（Y6090359, Y6090383）; Supported by the Department of Education of Zhejiang Province（Z200803357）

摘　　要：In this paper we obtain the fundamental solution for a class of weighted BaouendiGrushin type operator L_(p,γ,α)u = ▽_γ·(|▽_γu|^(p-2)ρ~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.In this paper we obtain the fundamental solution for a class of weighted BaouendiGrushin type operator Lp,γ,α u=△↓·（｜△↓γu｜^p-2ρ^α△↓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.

关 键 词：fundamental solution weighted Baouendi-Grushin type operator Hardy type inequality 

分 类 号：O178[理学—数学]