For an L²-bounded Calderón-Zygmund Operator T acting on , and a weight w ∈ A₂, the norm of T on L²(w) is dominated by . The recent theorem completes a line of investigation initiated by Hunt-Muckenhoupt-Wheeden in 1973 (MR0312139), 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 A₂ 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 Calderón-Zygmund theory. We survey the proof of this Theorem in this paper.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc95-0-7,
author = {Michael Lacey},
title = {The linear bound in A2 for Calderon-Zygmund operators: a survey},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {97-114},
zbl = {1241.42011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc95-0-7}
}
Michael Lacey. The linear bound in A₂ for Calderón-Zygmund operators: a survey. Banach Center Publications, Tome 95 (2011) pp. 97-114. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc95-0-7/