In this paper, we prove some new dynamic inequalities involving �− monotonic functions on time scales. Te main results will be proved by employing H¨ older’s inequality, integration by parts, and a chain rule on time scales. As a special case when T = R, our results contain the continuous inequalities proved by Heinig, Maligranda, Peˇ cari´c, Peri´ c, and Persson and when T = N, the results to the best of the authors’ knowledge are essentially new.