This paper introduced novel multidimensional Hardy-type inequalities with general kernels on time scales, extending existing results in the literature. We established generalized inequalities involving a general Hardy operator with multiple variables and kernels on arbitrary time scales. Our findings not only encompassed known results in the realm of real numbers ( $\mathbb{T}\mathbb{=}\mathbb{R}$), but also provided refinements and generalizations thereof. The proposed inequalities offered versatile applications in mathematical analysis and beyond, contributing to the ongoing exploration of inequalities on diverse time scales.

Some new reverse versions of Hilbert-type inequalities are studied in this paper. The results are established by applying the time scale versions of reverse Hölder's inequality, reverse Jensen's inequality, chain rule on time scales, and the mean inequality. As applications, some particular results (when $\mathbb{T}\mathbb{=}\mathbb{N}$ and $\mathbb{T}\mathbb{=}\mathbb{R}$) are considered. Our results provide some new estimates for these types of inequalities and improve some of those recently published in the literature.

In this study, we introduced several novel Hardy-type inequalities with negative parameters for monotone functions within the framework of delta calculus on time scales $\mathbb{T}$. As an application, when ${\mathbb{T}\mathbb{=}\mathbb{N}}_0,$ we derived discrete inequalities with negative parameters for monotone sequences, offering fundamentally new results. When $\mathbb{T}\mathbb{=}\mathbb{R},$ we established continuous analogues of inequalities that have appeared in previous literature. Additionally, we presented inequalities for other time scales, such as $\mathbb{T}=q^{{\mathbb{N}}_0}$ for $q>1,$ which, to the best of the authors' knowledge, represented largely novel contributions.