Gaussians Do Not Always Maximize Mixed-Norm Strichartz Inequalities for the Schrödinger Equation

We investigate the maximization problem for the family of mixed-norm Strichartz inequalities for the Schrödinger equation, $\|e^{-itΔ/2}f\|_{L_t^qL_{\boldsymbol{x}}^r(\mathbb{R}^{1+d})}\le C_{q,r}\lVert f\rVert_{L^2(\mathbb{R}^d)}$, with $2/q+d/r=d/2$, $q,r\geq 2$, and thus $r\leq 2d/(d-2)$ if $d\ge