Hardy's type integral inequalities on time scales

In this paper, we prove some new integral inequalities of Hardy's type on time scales. The Hardy inequalities have many applications especially in proving the boundedness Cesáro operators. The main results will be proved by making use of some algebraic inequalities, the Hölder inequality and a simple consequence of Keller's chain rule on time scales. The discrete inequalities that we will derive from our results in the discrete time scales are essentially new.