Hardy-Leindler Type Inequalities on Time Scales

In this paper, we will prove some new dynamic inequalities on a time scale T. These inequalities, as special cases, when T = R contain some integral inequalities and when T = N contain the discrete inequalities due to Leindler. The main results will be proved by using the Holder inequality and a simple consequence of Keller's chain rule on time scales. From our results, as applications, we will derive some new continuous and discrete Wirtinger type inequalities. The technique in this paper is completely different from the technique used by Leindler to prove his main results.