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

Banach Center Publications (2011)

- Volume: 95, Issue: 1, page 97-114
- ISSN: 0137-6934

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topMichael 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 -

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