I am reading Functional Analysis, Sobolev Spaces and Partial Differential Equations, by Haim Brezis.
Corollary $9.13$ says (Among other results)
For $m \geq 1, \quad W^{m,p}(\mathbb{R}^n) \hookrightarrow L^{\infty}(\mathbb{R}^n) \qquad \text{if} \ \frac{1}{p} < \frac{m}{n} \qquad (*)$
And the proof says:
The result can be obtained by repeated applications of Morrey's Theorem, which precisely says:
If $p >n$ then $\quad W^{1,p}(\mathbb{R}^n) \hookrightarrow L^{\infty}(\mathbb{R}^n) $
I haven't been able to show the Embedding $(*)$ by "aplicating Morrey's theorem", because I cannot conclude that $p>n$.
For example, if $m=3, n=3$ and $p=2$, then we have $\frac{1}{p}=\frac{1}{2} < \frac{3}{3}= \frac{m}{n}$. $(*)$ says we have the embedding: $$W^{3,2}(\mathbb{R}^3) \hookrightarrow L^{\infty}(\mathbb{R}^3)$$
But definitely we cannot apply (At least trivially) Morrey's theorem because $ 2 \ngtr 3$. We would need to conclude first that for $u \in W^{3,2}(\mathbb{R}^3)$ then $u \in W^{1,\tilde{p}}(\mathbb{R}^3)$ for a $\tilde{p} >3$.