Higher integrability theorems on time scales from reverse Hölder's inequalities

Abstract

In this paper, we establish some new reverse dynamic inequalities and use them to prove some higher integrability theorems for decreasing functions on time scales. In order to derive our main results, we first prove a new dynamic inequality for convex functions related to the inequality of Hardy, Littlewood and P?lya, known from the literature. Then, we prove a refinement of the famous Hardy inequality on time scales for a class of decreasing functions. As an application, our results are utilized to formulate the corresponding reverse integral and discrete inequalities, which are essentially new.