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

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