The linear bound in A₂ for Calderón-Zygmund operators: a survey

Michael Lacey. "The linear bound in A₂ for Calderón-Zygmund operators: a survey." Banach Center Publications 95.1 (2011): 97-114. <http://eudml.org/doc/281645>.

@article{MichaelLacey2011,
abstract = {For an L²-bounded Calderón-Zygmund Operator T acting on $L²(ℝ^\{d\})$, and a weight w ∈ A₂, the norm of T on L²(w) is dominated by $C_T ||w||_\{A₂\}$. 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.},
author = {Michael Lacey},
journal = {Banach Center Publications},
keywords = { conjecture; sharp weighted inequality},
language = {eng},
number = {1},
pages = {97-114},
title = {The linear bound in A₂ for Calderón-Zygmund operators: a survey},
url = {http://eudml.org/doc/281645},
volume = {95},
year = {2011},
}

TY - JOUR
AU - Michael Lacey
TI - The linear bound in A₂ for Calderón-Zygmund operators: a survey
JO - Banach Center Publications
PY - 2011
VL - 95
IS - 1
SP - 97
EP - 114
AB - For an L²-bounded Calderón-Zygmund Operator T acting on $L²(ℝ^{d})$, and a weight w ∈ A₂, the norm of T on L²(w) is dominated by $C_T ||w||_{A₂}$. 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.
LA - eng
KW - conjecture; sharp weighted inequality
UR - http://eudml.org/doc/281645
ER -