Reinforcing a Philosophy: Littlewood--Paley theory for the moment curve over generic local fields

Abstract

Using the Girard--Newton formulae, I give a simple proof of isotropic square function estimates for extension operators along the moment curve in generic local fields. Using Bezout's Theorem and the Implicit Function Theorem, I give an alternate, sharper proof for real or complex non-degenerate, polynomial curves.

arXiv comment10 pages, related to arXiv:1906.05877, arXiv:2201.09649 and arXiv:2203.13644, comments welcome :) Small improvements to the exposition have been made including clarifying the dependence on the dimension in the relevant bounds (e.g., Theorem 1; thanks to Trevor Wooley for pointing this out to me). A section at the end of the paper dicussing the connection to Superorthogonality has been added