In this paper, we establish some dynamic Hilbert-type inequalities in two independent variables on time scales by using the Fenchel–Legendre transform. We also apply our inequalities to discrete and continuous calculus to obtain some new inequalities as particular cases. Our results give more general forms of several previously established inequalities.

中文翻译：

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涉及Fenchel-Legendre变换的两个自变量中的新动态希尔伯特型不等式

在本文中，我们通过使用Fenchel-Legendre变换在时间尺度上的两个自变量中建立了一些动态的希尔伯特型不等式。我们还将不等式应用于离散和连续演算，以获取一些新的不等式作为特殊情况。我们的结果给出了一些先前建立的不等式的更一般形式。