Using the factorizations of suitable operators, we establish several identities that give simple and direct understandings as well as provide the remainders and “virtual” optimizers of several the Hardy and Hardy–Rellich type inequalities.

中文翻译：

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通过分解使贝塞尔对改善了Hardy和Hardy-Rellich类型不等式

通过使用合适运算符的因式分解，我们建立了一些标识，这些标识可以提供简单直接的理解，并提供一些Hardy和Hardy-Rellich类型不等式的余数和“虚拟”优化器。