Jaehoon Shin

Sharp helical maximal estimates in all dimensions

We establish sharp $L^p$ maximal estimates for averages over smooth nondegenerate curves in $\mathbb R^n$ for $p>n$. More precisely, we show that for any nondegenerate curve $\gamma$ in $\mathbb R^n$ and the associated maximal operator \begin{equation} M f(x):=\sup_{t>0} \Big|\int_{-1}^1f(x-t\gamma(s))\chi(s)\,\mathrm{...