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Abstract Let and . We characterize the validity of the inequality for the composition of the Hardy operator, for all non‐negative measurable functions on , . We construct a more straightforward discretization method than those previously presented in the literature, and we provide some new scales of weight characterizations of this inequality in both discrete and continuous forms and we obtain previous characterizations as the special case of the parameter.
Гогатишвили et al. (Thu,) studied this question.