I would like to show this inequality. I need help to show this inequality
Let $F(\Phi)=\left|\Phi\right|^{\alpha}\Phi$ with even integer $\alpha>0$. Let $k$ be a positive integer satisfying $[([n/2]+1+k)/2]+1\leq k.$ We put $N:=[n/2]+1+k.$ Then, \begin{equation} \left\|F(\Phi)\right\|_{W^{N,2}(\mathbb{R}^n)}\leq C\left\|\Phi\right\|^{\alpha}_{W^{k,\infty}(\mathbb{R}^n)}\left\|\Phi\right\|_{W^{N,2}(\mathbb{R}^n)}, \end{equation} where $C$ is a positive constant.
Here [s] defines the integer part of s.