Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 163 / 4 / a

Let $\Theta (R)$ partition an $R^{-1}$-neighborhood of the parabola into $R^{-1/2}\times R^{-1}$ caps, and suppose ${\hat{f}}_{\theta }$ is supported in $\theta$. The decoupling inequality for the parabola states that for $2\le p<\infty$ and every $ϵ>0$,

Solved by gpt-5.6-sol high.