In this paper, we extend the Minkowski integral inequality on time scales by \( \varDelta \varDelta \)-integral and the inverse Minkowski inequality over the set of constant sign functions. We get similar results by replacing \( \varDelta \varDelta \)-integral with \( \varDelta \nabla \), \( \nabla \varDelta \) and \( \nabla \nabla \)-integrals. For application, we give another proof of the Hardy inequality on time scales according to the Minkowski inequality.

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有关时间尺度上的Minkowski和Hardy积分不等式的更多信息

在本文中，我们在时间尺度上通过\（\ varDelta \ varDelta \）-积分和恒定符号函数集上的Minkowski不等式逆扩展了Minkowski积分不等式。通过将\（\ varDelta \ varDelta \）-integral替换为\（\ varDelta \ nabla \），\（\ nabla \ varDelta \）和\（\ nabla \ nabla \）- integral，我们得到类似的结果。对于应用，我们根据Minkowski不等式在时间尺度上给出了Hardy不等式的另一种证明。