与广义Baouendi-Grushin向量场相联系的Hardy不等式及其应用

本文建立一类与广义Baouendi—Grushin向量场联系的Hardy不等式．采用的技巧是延伸欧氏空间上的散度定理推出的基本积分不等式和选定适当的向量场．Hardy不等式相应的最佳常数也得到证明．本文结果包括了已有广义Baouendi-Grushin向量场的Hardy不等式．作为应用，讨论了由Baouendi-GrusMn向量场构成一退化次椭圆算子的一些性质和刻画了这类向量场构成的非线性算子的一个正解．

Hardy Inequalities and Applications Related to Generalized Baouendi-Grushin Vector Fields

In this paper we establish a class of Hardy inequalities related to the gen- eralized Baouendi-Grushin vector fields from another view. Our technique is based on an extension of an elementary integral inequality in the Euclidean space by the generalized di- vergence theorem, and then the choice of suitable vector fields. The best constant is also discussed. Our results contain the well known Hardy inequalities for the class of vector fields. As immediate consequences, we discuss some properties for p-degenerate subelliptic opera- tor and characterize a positive solutions of the nonlinear operator constructed by generalized Baouendi-Grnshin vector fields.