The main objective of the present paper is an extension of several classical integral Hardy-type inequalities with kernels to a time scales setting. The established inequalities refer to a class of monotone functions and they are characterized by appropriate relations for the accompanying weight functions. As an application, we obtain the corresponding discrete Hardy-type inequalities for monotone sequences, which are essentially new.

中文翻译：

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一些新的动态 Hardy 型不等式，其核涉及单调函数

本文的主要目标是将几个经典的带有核的哈代积分型不等式扩展到时间尺度设置。建立的不等式是指一类单调函数，它们的特点是与伴随的权重函数有适当的关系。作为应用，我们获得了单调序列的相应离散 Hardy 型不等式，它们本质上是新的。