In this paper, we provide a new extension of Hardy-Hilbert’s inequality with the kernel consisting of double power functions and derive its equivalent forms. The obtained inequalities are then further discussed regarding the equivalent statements of the best possible constant factor related to several parameters. The operator expressions of the extended Hardy-Hilbert’s inequality are also considered.

中文翻译：

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包含双幂函数核的Hardy-Hilbert不等式的新扩展

在本文中，我们用包含双幂函数的核提供了Hardy-Hilbert不等式的新扩展，并推导了其等效形式。然后，关于与几个参数有关的最佳可能常数因子的等效表述，进一步讨论获得的不等式。还考虑了扩展的Har​​dy-Hilbert不等式的算子表达式。