Gaussian extremizer conjecture for the Schrödinger Strichartz estimate

Let $2\leq p,q\leq\infty$ and let $d$ be the spatial dimension. For $f\in L^2(\mathbb{R}^d)$, consider the Schrödinger Strichartz estimate

$$\|\|e^{it\Delta}f\|_{L^p(\mathbb{R}^d)}\|_{L^q(\mathbb{R})}\leq C\|f\|_{L^2(\mathbb{R}^d)},$$

where $\Delta$ is the Laplacian and

$$\frac{d}{p}+\frac{2}{q}=\frac{d}{2},\qquad (p,q,d)\neq(\infty,2,2).$$

Gaussian extremizer conjecture. A function $f(\boldsymbol{x})$ maximizes the Strichartz estimate if and only if it has the form

$$f(\boldsymbol{x})=Ae^{-B\|\boldsymbol{x}\|^2+\boldsymbol{u}\cdot\boldsymbol{x}},$$

where $A,B\in\mathbb{C}$, $\operatorname{Re}B>0$, and $\boldsymbol{u}\in\mathbb{C}^d$. This conjecture identifies all extremizers of the space-time Strichartz inequality; it arose from the search for maximizers following Strichartz's original work. The supplied text does not state whether it has been resolved.