New Dynamic Inequalities for Decreasing Functions and Theorems of Higher Integrability

Abstract

In this paper we establish some new dynamic inequalities on time scales which contain in particular generalizations of integral and discrete inequalities due to Hardy, Littlewood, Pόlya, D’Apuzzo, Sbordone and Popoli. We also apply these inequalities to prove a higher integrability theorem for decreasing functions on time scales.