中文摘要：

该文主要考虑与Jacobi算子相关的Hardy不等式. 主要结果之一是求得了相关不等式的最佳常数. 作为该不等式的应用之一，该文证明了，不同于欧式空间情形，双曲空间上的Hardy 不等式可以整体的增添Brezis-Vázquez型余项.

英文摘要：

In this paper we consider the Hardy inequalities for Jacobi operators. We compute the sharp constants of these inequalities. As an application, we show the Hardy inequalities on hyperbolic spaces can be globally refined by adding remainder terms like the Brezis-V~zquez improvement, which is contrary to the case of Euclidean spaces.