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...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.展开更多
In this paper, properties of the spherical functions and Hardy-Sobolev inequalities of generalized Baouendi-Grushin vector fields are established, and then some unique continuation results for generalized Baouendi Gru...In this paper, properties of the spherical functions and Hardy-Sobolev inequalities of generalized Baouendi-Grushin vector fields are established, and then some unique continuation results for generalized Baouendi Grushin operators with singular weights are given.展开更多
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)
文摘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.
基金Supported by National Natural Science Foundation of China (Grant No. 10871157), Research Fund for the Doctoral Program o[ Higher Education of China (Grant No. 200806990032)
文摘In this paper, properties of the spherical functions and Hardy-Sobolev inequalities of generalized Baouendi-Grushin vector fields are established, and then some unique continuation results for generalized Baouendi Grushin operators with singular weights are given.