The aim of this article is to prove some new dynamic inequalities of Hardy type on time scales with several functions. Our results contain some results proved in the literature, which are deduced as limited cases, and also improve some obtained results by using weak conditions. In order to do so, we utilize Hölder’s inequality, the chain rule, and the formula of integration by parts on time scales.

中文翻译：

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在时标上具有Hardy类型的几个函数的一些新的动态不等式

本文的目的是在具有多个函数的时标上证明Hardy类型的一些新的动态不等式。我们的结果包含一些在文献中证明的结果，这些结果被推论为有限的情况，并且还可以通过使用弱条件来改善一些获得的结果。为此，我们利用了Hölder不等式，链式规则以及按时标划分的积分公式。