Sharp weighted estimates for approximating dyadic operators
Sharp weighted estimates for approximating dyadic operators
We give a new proof of the sharp weighted $L^p$ inequality$ |\|T\||_{L^p(w)} \leqC_{n,T}[w]_{A_p}^{\max(1,\frac{1}{p-1})}, $where $T$ is the Hilbert transform, a Riesz transform, theBeurling-Ahlfors operator or any operator that can be approximatedby Haar shift operators. Our proof avoids the Bellman functiontechnique and two weight norm inequalities. We use instead a recentresult …