Restriction of the Fourier transform to some oscillating curves

Xianghong Chen, Dashan Fan, Lifeng Wang

Let $\varphi$ be a smooth function on a compact interval $I$. Let $$\gamma (t)=\left(t,t^2,\cdots ,t^{n-1},\varphi (t)\right).$$ In this paper, we show that $$\left(\int_I \big|\hat f(γ(t))\big|^q \b…