# Sharp A 2 inequality for Haar shift operators

Research output: Contribution to journal › Article › peer-review

## Standard

**Sharp A 2 inequality for Haar shift operators.** / T. Lacey, Michael; Petermichl, Stefanie; Reguera, Maria Carmen.

Research output: Contribution to journal › Article › peer-review

## Harvard

*Mathematische Annalen*, vol. 348, pp. 127. https://doi.org/10.1007/s00208-009-0473-y

## APA

*Mathematische Annalen*,

*348*, 127. https://doi.org/10.1007/s00208-009-0473-y

## Vancouver

## Author

## Bibtex

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## RIS

TY - JOUR

T1 - Sharp A 2 inequality for Haar shift operators

AU - T. Lacey, Michael

AU - Petermichl, Stefanie

AU - Reguera, Maria Carmen

N1 - 14 pages, submitted to math annalen. Typos corrected. This is the final version of the paper

PY - 2009/6/10

Y1 - 2009/6/10

N2 - As a corollary to our main theorem we give a new proof of the result that the norm of the Hilbert transform on L^2(w) has norm bounded by a the A_2 characteristic of a weight to the first power, a theorem of one of us. This new proof begins as the prior proofs do, by passing to Haar shifts. Then, we apply a deep two-weight T1 theorem of Nazarov-Treil-Volberg, to reduce the matter to checking a certain carleson measure condition. This condition is checked with a corona decomposition of the weight. Prior proofs of this type have used Bellman functions, while this proof is flexible enough to address all Haar shifts at the same time.

AB - As a corollary to our main theorem we give a new proof of the result that the norm of the Hilbert transform on L^2(w) has norm bounded by a the A_2 characteristic of a weight to the first power, a theorem of one of us. This new proof begins as the prior proofs do, by passing to Haar shifts. Then, we apply a deep two-weight T1 theorem of Nazarov-Treil-Volberg, to reduce the matter to checking a certain carleson measure condition. This condition is checked with a corona decomposition of the weight. Prior proofs of this type have used Bellman functions, while this proof is flexible enough to address all Haar shifts at the same time.

KW - math.CA

KW - 42

U2 - 10.1007/s00208-009-0473-y

DO - 10.1007/s00208-009-0473-y

M3 - Article

VL - 348

SP - 127

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

ER -