Small cap decoupling for the paraboloid in $\mathbb{R}^n$

TL;DR

This paper extends the small cap decoupling theory for paraboloids in higher-dimensional Euclidean spaces, broadening the understanding of decoupling inequalities in harmonic analysis.

Contribution

It generalizes the small cap decoupling results to paraboloids in r^n for certain p ranges, advancing the theoretical framework.

Findings

Extended decoupling inequalities to higher dimensions

Identified new p ranges for applicability

Enhanced understanding of harmonic analysis techniques

Abstract

We extend the small cap decoupling program established by Demeter, Guth, and Want to paraboloids in $\mathbb{R}^n$ for some range of $p$.