Cone restriction conjecture for the wave equation

Let $u$ solve the wave equation on $\mathbb{R}\times\mathbb{R}^n$ with initial data $u(0,x)=0$ and $u_t(0,x)=f(x)$. The solution is expressed through the half-wave oscillatory integrals, and for $\widehat f$ define

$$\|u(t,x)\|_{L^q_{t,x}(\mathbb{R}\times\mathbb{R}^n)}\leq C_{p,q,n}\|\widehat f\|_{L^p_{1/|\xi|}(\mathbb{R}^n)}.$$

Here $L^p_{1/|\xi|}(\mathbb{R}^n)$ denotes the $L^p$ space with measure $\mathrm{d}\xi/|\xi|$. Wave-equation cone restriction conjecture. The estimate holds if and only if

$$q>\frac{2n}{n-1}\quad\text{and}\quad\frac{n+1}{q}=\frac{n-1}{p'}.$$

This is the noncompact-cone version of the cone restriction conjecture and is closely related to spacetime estimates for the wave equation. The source presents it as an open formulation, with the corresponding compact-cone conjecture still open in dimensions $n\geq 5$.