Decoupling for AD-regular sets on the parabola
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 Szemerédi--Trotter-type estimates into the bootstrapping argument from BD. As an application, our results complement, and in some cases improve earlier results chang2022decoupling for arithmetic Cantor sets.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.