Some new characterizations of weights for hardy-type inequalities with kernels on time scales

Abstract In this paper, we present novel characterizations of weight functions for Hardy-type dynamic inequalities involving kernels on an arbitrary time scale 𝕋. We establish both necessary and sufficient conditions for a specific class of kernels. As a special case, when 𝕋 = ℕ, our results reduce to the classical discrete inequalities proved by Okpoti et al., while in the continuous case 𝕋 = ℝ, the resulting inequalities are essentially new.