Let $H = L^2((0,1)^2)$, and let $$V = \{f\in H: \exists g\in L^2(0,1): f(x,y)=g(x) \}$$
I've already prooved that V is a closed subspace of H.

Now i want to find the orthogonal projection of $f(x,y)=xy$ in V, the problem is that i don't know how to aproach the problem.
I've seen similar exercises, but for subspaces with finite dimension, wich is not this case. 
Any ideas on how to start solving this?
Thanks