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arXiv · 1001.4724

Sharp weighted estimates for approximating dyadic operators

David Cruz-Uribe·Jose Maria Martell·Carlos Perez
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Abstract

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.

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David Cruz-Uribe, Jose Maria Martell, Carlos Perez. 2010-03-05. Sharp weighted estimates for approximating dyadic operators. https://doi.org/10.3934/era.2010.17.12

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