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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 $\mathbb{T}=\mathbb{N}$ .

New characterizations of weights on dynamic inequalities involving a Hardy operator