On Jensen-type inequalities for nonsmooth radial scattering solutions of a loglog energy-supercritical Schrodinger equation

Given $n\in \{3,4\}$ (resp. $n=5$) and $k>1$ (resp. $\frac{4}{3} > k > 1$),weprovescatteringoftheradial$\tilde{H}^{k}:= \dot{H}^{k}($\mathbb{R}$^{n}) \cap \dot{H}^{1}($\mathbb{R}$^{n})$ solutions of the loglog energy-supercritical Schrodinger equation $i \partial_{t} u + \triangle u = |u|^{\frac{4}{n-2}}u log^{\gamma} (\log( 10 + |u|^{2} ))$for$0 < \gamma < \gamma_{n}$. In order to control the barely supercritical nonlinearity for nonsmooth solutions, i.e solutions with data in ${\tilde{H}}^k$, $k \leq \frac{n}{2}$, we prove some Jensen-type inequalities.