  We give a new proof of the sharp weighted $L^2$ inequality ||T||_{L^2(w)}
\leq c [w]_{A_2} where $T$ is the Hilbert transform, a Riesz transform, the
Beurling-Ahlfors operator or any operator that can be approximated by Haar
shift operators. Our proof avoids the Bellman function technique and two weight
norm inequalities. We use instead a recent result due to A. Lerner to estimate
the oscillation of dyadic operators.
