广义HEISENBERG-GREINER p-退化椭圆算子的一类带有余项的含权Hardy不等式  

A Class of Weighted Hardy Inequalities with Remainder Terms for Generalized p-degenerate Sub-elliptic Heisenberg-Greiner Operators

作　　者：王胜军 韩亚洲 WANG Shengjun;HAN Yazhou(School of Mathematics and Statistics,Qinghai Normal University,Xining 810008,China;Department of Mathematics,College of Science,China Jiliang University,Hangzhou 310018,China)

机构地区：[1]青海师范大学数学与统计学院,西宁810008 [2]中国计量大学理学院,杭州310018

出　　处：《西南大学学报（自然科学版）》2022年第5期89-96,共8页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(11201443).

摘　　要：研究了广义Heisenberg-Greiner p-退化椭圆算子的一类带有余项的含权Hardy不等式的推广问题.利用散度定理并选择恰当的向量场,得到一类带有余项的含权Hardy不等式.结合逼近的方法,给出了最佳常数的证明,进一步推广了已有的结果.In this paper,we present the improved versions of weighted Hardy inequalities with remainder terms for the generalized p-degenerate sub-elliptic Heisenberg-Greiner operators.By employing divergence theorem and choosing suitable vector fields,we obtained some weighted Hardy inequalities with remainder terms.Furthermore,the proof ofthe best constants is given by combining with the approximation method,which extend the existing results.

关 键 词：广义Heisenberg-Greiner p-退化椭圆算子 带有余项的含权Hardy不等式 最佳常数 

分 类 号：O175.25[理学—数学]