Reflexivity of $L^2(W^{1,2})$

Question

Consider the space $L^2(0,T;W^{1,2}(B))$ where $B$ is the unit ball in $\mathbb R^3$. Is it reflexive?

I know that sobolev spaces and $L^p$ spaces are reflexive for $1<p<\infty$. I am guessing this to be reflexive also but couldn't prove it. Any help is appreciated.

Don't want a proof. Just a strategy or some hints.

Answer 1

Hint 1:

The norm in this space has a very special property.

Hint 2:

Hilbert space.