New characterizations of weights on dynamic inequalities involving a Hardy operator

Abstract

Abstract In this paper, we establish some new characterizations of weighted functions of dynamic inequalities containing a Hardy operator on time scales. These inequalities contain the characterization of Ariňo and Muckenhoupt when T = R $\mathbb{T}=\mathbb{R}$ , whereas they contain the characterizations of Bennett–Erdmann and Gao when T = N $\mathbb{T}=\mathbb{N}$ .

Keywords

• Hardy type inequality
• Hardy’s operator
• Time scales
• Weighted functions
• Inequalities