Sharp weighted estimates for approximating dyadic operators

Details Sharp weighted estimates for approximating dyadic operators Sharp weighted estimates for approximating dyadic operators

2010-01-26

arxiv.org/abs/1001.4724v2

Mathematics

Classical Analysis and ODEs

To appear in the Electronic Research Announcements in Mathematical Sciences

Scientific paper

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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