Heisenberg群上p-sub-Laplace算子的一类Hardy型不等式及其应用

Hardy Type Inequalities and Applications for p-Sub-Laplace Operator on the Heisenberg Group

利用正则化及逼近的方法,获得了Heisenberg群上p-sub-Laplace算子的一类强Hardy不等式,推广了已有文献中p的取值范围,并进一步弥补了去除原点的缺陷.作为应用,讨论了与该算子相关的一类非线性算子的正定性与下无界性,并给出了它的一个正解.

Using regularization method and the approximating method to p-sub-Laplace operator on the- Heisenberg group, one gets the conclusion of sharp Hardy inequality for the operator. The results improve the range of the p and remedy a defect that eliminate the zero point in the existed results. As applications, one discusses the positive property and the unbounded property from below for p-degenerate subelliptic operator and characterize a positive solutions of the nonlinear operator constructed by p-sub-Laplace operator on theHeisenberg group.