Convolution estimates for measures on some complex curves (Q2420259)

In the paper under review, a bounded complex curve $\Gamma$ along with the affine arclength measure $\mathrm{d}\mu$ on it was considered. The authors then consider the convolution operator along $\Gamma$ with respect to $\mathrm{d}\mu$. For all locally finitely type complex curves in $\mathbb{C}^3$ and monomial curves with the equation $(z, \dots, z^{d-1}, z^N)$ in $\mathbb{C}^d$ for $d \geq 4$, they prove an estimate in Lorentz spaces concerning this operator with almost sharp exponents.