A Convolution Estimate for a Measure on a Curve in R^4

Daniel M. Oberlin

Let $\gamma(t)=(t,t^2,t^3,t^4)$ and fix an interval $I\subset{\Bbb R}$. If $T$ is the operator on ${\Bbb R}^4$ defined by $Tf(x)=\int\nolimits_If(x-\gamma(t))\,dt$, then $T$ maps $L^{5\over 3}({\Bbb R}^4)$ into $L^2({\Bbb R}^4)$.