The Linear Bound in A_2 for Calder\'on-Zygmund Operators: A Survey
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.
Keywords
Cite
@article{arxiv.1011.5784,
title = {The Linear Bound in A_2 for Calder\'on-Zygmund Operators: A Survey},
author = {Michael T Lacey},
journal= {arXiv preprint arXiv:1011.5784},
year = {2010}
}
Comments
19 pages. Submitted to the proceedings of the Jozef Marcinkiewicz Centenary Conference