Decoupling for AD-regular sets on the parabola
Classical Analysis and ODEs
2026-05-26 v1
Abstract
We improve the decoupling exponent for functions with spectrum inside AD-regular collections of arcs on the parabola. We achieve this by incorporating recent Szemer\'{e}di--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.
Keywords
Cite
@article{arxiv.2605.24109,
title = {Decoupling for AD-regular sets on the parabola},
author = {Ciprian Demeter and Yuqiu Fu},
journal= {arXiv preprint arXiv:2605.24109},
year = {2026}
}