A Hardy-Sobolev inequality for the twisted Laplacian

被引:4
|
作者
Adimurthi [1 ]
Ratnakumar, P. K. [2 ,3 ]
Sohani, Vijay Kumar [4 ]
机构
[1] Tata Inst Fundamental Res, Ctr Applicable Math, Bangalore 560065, Karnataka, India
[2] Harish Chandra Res Inst, Chhatnag Rd, Allahabad 211019, Uttar Pradesh, India
[3] Homi Bhabha Natl Inst, Training Sch Complex, Mumbai 400085, Maharashtra, India
[4] Indian Inst Sci, Dept Math, Bangalore 560012, Karnataka, India
关键词
Hardy-Sobolev inequality; fundamental solution; twisted Laplacian; special Hermite expansion;
D O I
10.1017/S0308210516000081
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We prove a strong optimal Hardy-Sobolev inequality for the twisted Laplacian on C-n. The twisted Laplacian is the magnetic Laplacian for a system of n particles in the plane, corresponding to the constant magnetic field. The inequality we obtain is strong optimal in the sense that the weight cannot be improved. We also show that our result extends to a one-parameter family of weighted Sobolev spaces.
引用
收藏
页码:1 / 23
页数:23
相关论文
共 50 条