Sharp maximal function estimates for Hilbert transforms along monomial curves in higher dimensions

Renhui Wan

For any nonempty set $U\subset {\mathbb{R}}^{+}$, we consider the maximal operator $\h^U$ defined as $\h^Uf=\sup_{u\in U}|H^{(u)} f|$, where $H^{(u)}$ represents the Hilbert transform along the…