中文摘要：

在海森堡组的设置，基于旋转方法，我们获得锋利(p， p ) 为强壮的操作符的估计。L ^p ( ⁿ ) 上的强壮的操作员的标准仍然是 p/(p-1 ) ，这将被显示出。这去暗示尽管有领域，强壮的操作员的 L ^p 标准是一样的某方法是间隔在上，在海森堡上的 ⁿ , 或椭圆体的球组织 ⁿ 。由构造一个特殊函数，我们在弱类型发现最好的常数(1， 1 ) 为强壮的操作符的不平等。用翻译途径，我们从 H ¹ 为强壮的操作员建立固定到 L ¹ 。而且，我们描述 M _p 重量和 A _p 重量之间的差别并且用加权的强壮的不平等获得如此的重量的描述。

英文摘要：

In the setting of the Heisenberg group, based on the rotation method, we obtain the sharp （p,p） estimate for the Hardy operator. It will be shown that the norm of the Hardy operator on LP（Hn） is still p/（p- 1）. This goes some way to imply that the Lp norms of the Hardy operator are the same despite the domains are intervals on R, balls in Rn, or ‘ellipsoids＇ on the Heisenberg group Hn. By constructing a special function, we find the best constant in the weak type （1, 1） inequality for the Hardy operator. Using the translation approach, we establish the boundedness for the Hardy operator from H1 to L1. Moreover, we describe the difference between Mp weights and Ap weights and obtain the characterizations of such weights using the weighted Hardy inequalities.