与广义Baouendi-Grushin向量场相联系的加权Hardy-Sobolev不等式及其应用(英文)

Weighted Hardy-Sobolev Type Inequality for Generalized Baouendi-Grushin Vector Fields and Its Application

推广了一类与广义Baouendi-Grushin向量场相联系的Caffarelli-Kohn-Nirenberg不等式.首先借助Chern和Lin的思想,引进了一个函数变换;结合一些基本的不等式和精确估计,建立了一类加权的Hardy-Sobolev不等式;然后证明了这类与广义Baouendi-Grushin向量场相联系的Caffarelli-Kohn-Nirenberg不等式.

This work is devoted to generalizing a class of Caffarelli-Kohn-Nirenberg type inequalities for the generalized Baouendi-Grushin vector fields.Inspired by the idea of Chern and Lin,a function transformation is introduced.Combining some elementary inequalities and accurate estimates,we establish a class of weighted Hardy-Sobolev type inequalities and then prove a class of Caffarelli-Kohn-Nirenberg type inequalities for the generalized Baouedi-Grushin vector fields.