It is true to write that
$W^{1,\infty}(]0,\infty[) \hookrightarrow C([0,\infty[)$ et $W^{1,1}(]0,\infty[) \hookrightarrow C([0,\infty[)$ ?
Thanks



Sobolev injections
Let $f$ be a fonction in $L^1(0,+\infty)$
with norm 1 and let us define for $x\ge 0$
$$
\phi(x)=\int\_x^1f(t) dt.
$$
Then $\phi$ is continuous since
$
-\phi(h)+\phi(0)=\int\_0^h f(t) dt,
$
which goes to 0 with $h$ from the Lebesgue Dominated Convergence Theorem.


