What is $H^1([0,1]) \otimes H^1([0,1])$?

What is $H^1([0,1]) \otimes H^1([0,1])$?

Let $H^1([0,1])$ denote the Sobolev space $H^1$ on the interval $[0,1]$.
What is $H^1([0,1]) \otimes H^1([0,1])$?
Here, $\otimes$ the tensor product of Hilbert spaces. In particular, how
is that object related to $H^1([0,1]^2)$?