Article Contents
Article Contents

# Sharp weighted estimates for approximating dyadic operators

• We give a new proof of the sharp weighted $L^p$ inequality

$|\|T\||_{L^p(w)} \leq C_{n,T}[w]_{A_p}^{\max(1,\frac{1}{p-1})},$

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 [15] to estimate the oscillation of dyadic operators.
The method we use is flexible enough to obtain the sharp one-weight result for other important operators as well as a very sharp two-weight bump type result for $T$ as can be found in [5].

Mathematics Subject Classification: 42B20, 42B25.

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