On the small cap decoupling for the moment curve in $\mathbb{R}^3$

TL;DR

This paper establishes precise small cap decoupling estimates for the moment curve in three-dimensional space, advancing understanding in harmonic analysis and decoupling theory within specific parameter ranges.

Contribution

It provides sharp small cap decoupling estimates for the moment curve in \\mathbb{R}^3, filling gaps in the parameter ranges for \\mathbb{R}^2 and \\mathbb{R}^3.

Findings

Sharp small cap decoupling estimates proved for the moment curve in \\mathbb{R}^3.

Results cover remaining small cap parameter ranges in \\mathbb{R}^2 and \\mathbb{R}^3.

Advances in harmonic analysis and decoupling theory.

Abstract

This paper proves sharp small cap decoupling estimates for the moment curve $\mathcal{M}^n=\{(t,t^2,\ldots,t^n):0\leq t\leq 1\}$ in the remaining small cap parameter ranges for $\mathbb{R}^2$ and $\mathbb{R}^3$.