We find the conditions for a compact Hardy operator in Lorentz spaces to belong to the operator ideals generated by sequences of \( s \)-numbers. We obtain some estimates of the norms of the Hardy operator in these ideals in terms of integral expressions depending on the weight functions of the operator.

中文翻译：

---

算子理想中 Hardy 算子范数的估计

我们发现洛伦兹空间中的紧哈代算子属于由\( s \)数字序列生成的算子理想的条件。我们根据算子的权重函数，以积分表达式的形式获得了这些理想中 Hardy 算子范数的一些估计。