各向异性Heisenberg群上一类强Hardy型不等式及其应用

Sharp Hardy Type Inequalities on Anisotropic Heisenberg Groups and Applications

通过推广、改进欧氏空间中的思想,对各向异性Heisenberg群上的Hardy型不等式给出了一个新证明.注意到原有许多结果中,由于使用方法的原因把原点排出在外,首先构造了一类C1向量场,结合逼近的思想不仅改进了这个缺陷而且得到常数cpQ,p的最佳性.作为应用,讨论了一类p次非线性算子的正定性与下无界性.

This paper presents a new proof of a class of Hardy type inequalities on anisotropic Heisenberg groups.Using regularization method by the careful choice of a suitable vector field in C^1 and the approximating method,the obtained results not only contain the well-known results for sublaplace operator but also remedy a defect that eliminates the zero point in the existing results.Furthermore,the results get the best constant c^pQ,p.As applications,the positive property and the unbounded property from below for p-degenerate subelliptic operator are discussed.