Let $U\subseteq\mathbb{R}^n$ be a Lipschitz domain. I know that we can embed $W^{1,\infty}(U)$ into $C^{0,1}(U)$ with the help of Morrey's inequality. I also know that it is (up to measure zero) possible to embed $W^{k,p}(U)$ into $C^{k-1-\left\lfloor\frac{n}{p}\right\rfloor, \gamma}(U)$, where $k\in\mathbb{N}$, $p\in[1,\infty)$ and $$ \gamma := \begin{cases} \left\lceil \frac{n}{p} \right\rceil-\frac{n}{p} & \text{if }\frac{n}{p}\notin\mathbb{Z}\\ \text{any value in $(0,1)$} & \text{otherwise} \end{cases} $$
But what about embedding $W^{k,\infty}(U)$ into $C^{k-1, \gamma}(U)$ (i.e. the case when $p=\infty$ and $k\ge2$)?
I'd think it is possible since Morrey's inequality holds for $p=\infty$ as well. But Evan's book made it really vague if such a case is included, while Adams' book and Leoni's just left this case out. Is it because it cannot be done?