Generalizations of Hilbert-type inequalities with a homogeneous kernel on time scales

Abstract This paper focuses on establishing new generalizations of Hilbert-type inequalities on arbitrary time scales. We present three main theorems on weighted integral inequalities involving a nonnegative homogeneous kernel. The proofs rely on several auxiliary lemmas together with the effective application of Hölder’s inequality. By specializing our results to the continuous time scale ( $\mathbb{T}=\mathbb{R}$ T = R ) and the discrete time scale ( $\mathbb{T}=\mathbb{N}$ T = N ), we derive a number of corollaries that unify and extend both classical and recent inequalities. Overall, this work contributes to the theory of integral inequalities by providing a broader framework and new analytical tools within the calculus on time scales.