  We prove that convolution with affine arclength measure on the curve
parametrized by $h(t) := (t,t^2,...,t^n)$ is a bounded operator from
$L^p(\mathbb{R}^n)$ to $L^q(\mathbb{R}^n)$ for the full conjectured range of
exponents, improving on a result due to M. Christ. We also obtain nearly sharp
Lorentz space bounds.
