Hardy型不等式的研究进展
Progress on Hardy-type Inequalities
摘要：
本文综述了我们在调和分析中的一个著名课题--Hardy型不等式方面的一些最新进展.在第一节中，我们回顾了最初的概率动机处理的稳定速度方面的$L^2$理论。福岛和Uemura（2003）的结果的一个关键应用。在第二节中，对非线性情形（一般的Hardy型不等式）给出了直接的解析证明。在最后一节中，说明了前两节中提出的基本估计仍然可以大大改进。
英文摘要：
This paper surveys some of our recent progress on Hardy-type inequa\-lities which consist of a well-known topic in Harmonic Analysis. In the first section, we recall the original probabilistic motivation dealing with the stability speed in terms of the $L^2$-theory. A crucial application of a result by Fukushima and Uemura (2003) is included. In the second section, the non-linear case (a general Hardy-type inequality) is handled with a direct and analytic proof. In the last section, it is illustrated that the basic estimates presented in the first two sections can still be improved considerably.
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