Characterizations of weighted dynamic Hardy-type inequalities with higher-order derivatives

Abstract

Abstract In this paper, we establish some necessary and sufficient conditions for the validity of a generalized dynamic Hardy-type inequality with higher-order derivatives with two different weighted functions on time scales. The corresponding continuous and discrete cases are captured when T = R $\mathbb{T=R}$ and T = N $\mathbb{T=N}$ , respectively. Finally, some applications to our main result are added to conclude some continuous results known in the literature and some other discrete results which are essentially new.

Keywords

• Hardy’s inequality
• Higher-order derivatives
• Time scales