  We discuss weighted estimates for the squares of the Riesz transforms, R^{2},
on L^{2}(W) where W is a matrix A2 weight. We prove that if W is close to the
Identity matrix Id, then the operator norm of R^{2} is close to its unweighted
norm on L^{2} which is one. This is done by the use of the Bellman function
technique.
