Decoupling for AD-regular sets on the parabola

We improve the decoupling exponent for functions with spectrum inside AD-regular collections of arcs on the parabola. We achieve this by incorporating recent Szemerédi–Trotter-type estimates into the bootstrapping argument from \cite{BD}. As an application, our results complement, and in some cases improve earlier results \cite{chang2022decoupling} for arithmetic Cantor sets.