Heisenberg群上两类带权对数型Hardy-Sobolev不等式  

Two Classes of Weighted Logarithmic Hardy-Sobolev Inequalities on the Heisenberg Group

作　　者：张君丽 ZHANG Junli(School of Mathematics and Statistics,Northwestern Polytechnical University,Xi’an 710129,China)

机构地区：[1]西北工业大学数学与统计学院,西安710129

出　　处：《西安工业大学学报》2022年第4期353-360,共8页Journal of Xi’an Technological University

基　　金：国家自然科学基金(11771354)。

摘　　要：为研究Heisenberg群上两类带权对数型Hardy-Sobolev不等式,文中从次椭圆A-Laplace不等方程出发,利用欧氏空间的研究思路得出Heisenberg群上的Hardy型不等式,通过取满足假设条件的函数得出一类关于有紧支集的Lipschtz函数的带权对数型Hardy-Sobolev不等式;最终将假设条件减弱,得出另一类带权对数型Hardy-Sobolev不等式。This paper is devoted to studying two classes of weighted logarithmic Hardy-Sobolev inequalities on the Heisenberg group.Firstly,based on the idea of the Euclidean space,the Hardy-type inequality on the Heisenberg group is obtained from the Sub-elliptic A-Laplace inequality.Then a class of weighted logarithmic Hardy-Sobolev inequalities is deduced by taking the functions which satisfy the proper hypothesis.Finally,another class of weighted logarithmic Hardy-Sobolev inequalities can be gained by weakening the previous hypothesis.

关 键 词：HEISENBERG群 HARDY型不等式 Hardy-Sobolev不等式 A-Laplace不等方程 

分 类 号：O175.2[理学—数学]