In this paper, we obtain the best constant and the equality condition for a class of mixed-norm Hardy inequalities when the weight is a power function. By building and solving the corresponding Euler equation, we look for the best constant and the optimal function. One of the main ingredients is to introduce two key auxiliary functions so that the corresponding equalities are derived.

中文翻译：

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一类混合范数Hardy不等式的最佳常数问题

在本文中，当权重为幂函数时，我们获得了一类混合范数Hardy不等式的最佳常数和等式条件。通过建立和求解相应的欧拉方程，我们寻找最佳常数和最佳函数。主要成分之一是引入两个关键的辅助函数，以便得出相应的相等性。