Heisenberg型群上一类精确Hardy型不等式和Hardy-Sobolev型不等式及应用(英文)

Sharp Hardy Type Inequalities and Hardy-Sobolev Type Inequalities on Heisenberg Type Group and Applications

本文在Heisenberg型群上建立了一类精确的Hardy型不等式。采用的技巧是逼近及正则化的方法。进一步利用这个结果,本文建立了一类精确的Hardy-Sobolev型不等式。这两个结果包括了已有的相关结果。作为应用,讨论了一类具有Hardy位势的非线性算子的正定性与下无界性。

In this paper,using regularization and approximating method,we prove a Hardy type inequality which contains the origin and improves the range of the index p on Heisenberg type group.Furthermore,we use this result to estabhsh a Hardy-Sobolev type inequality.Our results contain the existed relevant results.As applications,we discuss the positive property and the unbounded property from below for a nonlinear operator relating with the Hardy potential.