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arXiv · 1011.5784

The Linear Bound in A_2 for Calder\'on-Zygmund Operators: A Survey

Michael T Lacey
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Abstract

For an L ^2-bounded Calderon-Zygmund Operator T, and a weight w \in A_2, the norm of T on L ^2 (w) is dominated by A_2 characteristic of the weight. The recent theorem completes a line of investigation initiated by Hunt-Muckenhoupt-Wheeden in 1973, has been established in different levels of generality by a number of authors over the last few years. It has a subtle proof, whose full implications will unfold over the next few years. This sharp estimate requires that the A_2 character of the weight can be exactly once in the proof. Accordingly, a large part of the proof uses two-weight techniques, is based on novel decomposition methods for operators and weights, and yields new insights into the Calder\'on-Zygmund theory. We survey the proof of this Theorem in this paper.

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Michael T Lacey. 2010-11-26. The Linear Bound in A_2 for Calder\'on-Zygmund Operators: A Survey. https://arxiv.org/abs/1011.5784

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