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

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