  Using Wilson's Haar basis in $\R^n$, which is different than the usual tensor
product Haar functions, we define its associated dyadic paraproduct in $\R^n$.
We can then extend "trivially" Beznosova's Bellman function proof of the linear
bound in $L^2(w)$ with respect to $[w]_{A_2}$ for the 1-dimensional dyadic
paraproduct. Here trivial means that each piece of the argument that had a
Bellman function proof has an $n$-dimensional counterpart that holds with the
same Bellman function. The lemma that allows for this painless extension we
call the good Bellman function Lemma. Furthermore the argument allows to obtain
dimensionless bounds in the anisotropic case.
