On The Best Constants Of Hardy Inequalities On Half Spaces In H-type Groups

Since Hardy gave his name to the Hardy inequality.More and more mathmatician pay attention to the varities of Hardy inequalities and from which derived all kinds of inequalities.Hardy inequalities and its improvement and generalization are also important in the study of linear and nonlinear partial differential equations.In addition,to seek the best constant related to Hardy inequalities is also one of the core content of mathematics study.This paper,we will focus on researching the problem of related best constants of Hardy inequalities on half spaces for Kohn's sublaplacian in H-type groups.Noticed that from Euclidean space to upper half-space of Euclidean,the best constants of Hardy inequalities has been jumped from (N-2)~2/4 to N~2/4,when singularity is located at the boundary.In this paper,by analyzing the properties of H-type groups and sublaplacian in H-type groups,and the polar coordinates conversion in H-type groups,using the methods of basic solution,analogying the Euclidean space,researching on the Hardy inequalities in H-type groups,and found that when the singularity is located at the boundary,the constants of Hardy inequalities also has been jumped.And this paper will prove that the constant related to the Hardy inequality is sharp.