与广义Baouendi-Grushin向量场相关的L^(p)加权Hardy型不等式

Weighted Hardy Type Inequalities Related to Generalized Baouendi-Grushin Vector Fields

研究与广义Baouendi-Grushin向量场相关的Lp加权Hardy型不等式.注意到已有结果通常对p限制为:1<p<Q或1<p<Q+α,α∈R,其中Q为齐次维数.本文通过改进Kombe的证明技巧,对1<p<+∞(p≠Q+α)和p=Q+α分别建立相应加权Hardy型不等式.

This paper is concerned with Lp weighted Hardy type inequalities related to generalized Baouendi-Grushin vector fields.We note that many known results require satisfying： 1 ＆lt; p ＆lt; Q or 1 ＆lt; p ＆lt; Q ＋ α,α∈R,where Q is the homogeneous dimension.By improving Kombe’s methods,the weighted Hardy inequalities are established for 1 ＆lt; p ＆lt; ＋ ∞（p≠Q ＋ α） and p = Q ＋ α,respectively.