A sharp square function estimate for the moment curve in ${\mathbb{R}}^n$

We use high-low frequency methods developed in the context of decoupling to prove sharp (up to $C_{\epsilon }{R}^{\epsilon }$) square function estimates for the moment curve $(t,t^2,\dots ,t^n)$ in ${\mathbb{R}}^n$. Our inductive scheme incorporates sharp square function estimates for auxiliary conical sets, which allows us to fully exploit lower dimensional information.