Refinement multidimensional dynamic inequalities with general kernels and measures

Abstract Using the properties of superquadratic and subquadratic functions, we establish some new refinement multidimensional dynamic inequalities of Hardy’s type on time scales. Our results contain some of the recent results related to classical multidimensional Hardy’s and Pólya–Knopp’s inequalities on time scales. To show motivation of the paper, we apply our results to obtain some particular multidimensional cases and provide refinements of some Hardy-type inequalities known in the literature.