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In this paper, we establish some reversed dynamic inequalities of Hilbert type on time scales nabla calculus by applying reversed Hölder's inequality, chain rule on time scales, and the mean inequality. As particular cases of our results (when T = N and T = R ), we get the reversed form of discrete and continuous inequalities proved by Chang-Jian, Lian-Ying and Cheung (Math. Slovaca 61(1):15–28, 2011). [ABSTRACT FROM AUTHOR]

Sharp remainder terms are explicitly given on the standard Hardy inequalities in $L^{p}(\mathbb {R}^{n})$ with $1< p< n$ . Those remainder terms provide a direct and exact understanding of Hardy type inequalities in the framework of equalities as well as of the nonexistence of nontrivial extremals. [ABSTRACT FROM AUTHOR]