Sharp superlevel set estimates for small cap decouplings of the parabola

Yuqiu Fu, Larry Guth, Dominique Maldague

We prove sharp bounds for the size of superlevel sets $\{x\in {\mathbb{R}}^2:|f(x)|>\alpha \}$ where $\alpha >0$ and $f:{\mathbb{R}}^2\to \mathbb{C}$ is a Schwartz function with Fourier transform s…