TITLE: Sobolev space reflexivity problem
QUESTION [6 upvotes]: Let $ I $ open interval of  $ \mathbb{R} $ 
We know that the Sobolev space $ W^{1, \infty}(I) $ is not reflexive. But, is there any easy proof of this result? 
Thank you in advance

REPLY [4 votes]: The space $W^{1,\infty}(I)$, $I = (a,b)$, is isomorphic to $\mathbb R \times L^\infty(I)$
via
$$v \mapsto (v(a), v').$$
Since $L^\infty(I)$ is not reflexive, $W^{1,\infty}(I)$ cannot be reflexive.