A Weighted Trudinger–Moser Inequality on R^N and Its Application to Grushin Operator |
| |
作者姓名: | Jia Jun WANG Qiao Hua YANG |
| |
作者单位: | School of Mathematics and Statistics |
| |
基金项目: | Supported by the National Natural Science Foundation of China (Grant No. 11201346) |
| |
摘 要: | Let x=(x',x')with x'∈Rk and x'∈R^N-k andΩbe a x'-symmetric and bounded domain in R^N(N≥2).We show that if 0≤a≤k-2,then there exists a positive constant C>0 such that for all x'-symmetric function u∈C0^∞(Ω)with∫Ω|■u(x)|^N-a|x'|^-adx≤1,the following uniform inequality holds1/∫Ω|x|^-adx∫Ωe^βa|u|N-a/N-a-1|x'|^-adx≤C,whereβa=(N-a)(2πN/2Γ(k-a/2)Γ(k/2)/Γ(k/2)r(N-a/2))1/N-a-1.Furthermore,βa can not be replaced by any greater number.As the application,we obtain some weighted Trudinger–Moser inequalities for x-symmetric function on Grushin space.
|
关 键 词: | Trudinger–Moser inequality Grushin operator sharp constant H-type group |
本文献已被 维普 SpringerLink 等数据库收录! |
| 点击此处可从《数学学报(英文版)》浏览原始摘要信息 |
| 点击此处可从《数学学报(英文版)》下载免费的PDF全文 |