2009
DOI: 10.1007/s00208-009-0473-y
|View full text |Cite
|
Sign up to set email alerts
|

Sharp A 2 inequality for Haar shift operators

Abstract: As a Corollary to the main result of the paper, we give a new proof of the inequalitywhere T is either the Hilbert transform ( Amer J Math 129 (5):1355-1375, 2007), a Riesz transform (Proc Amer Math Soc 136(4):1237-1249, 2008), or the Beurling operator (Duke Math J 112(2):281-305, 2002). The weight w is non-negative, and the linear growth in the A 2 characteristic on the right is sharp. Prior proofs relied strongly on Haar shift operators (CR Acad Sci Paris Sér I Math 330(6):455-460, 2000) and Bellman function… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
4
1

Citation Types

3
118
0

Year Published

2011
2011
2019
2019

Publication Types

Select...
5
1

Relationship

1
5

Authors

Journals

citations
Cited by 90 publications
(121 citation statements)
references
References 19 publications
3
118
0
Order By: Relevance
“…These auxiliary operators are already implicit in the original Nazarov-Treil-Volberg argument [22], and their more explicit form was identified in my extension of their result to the vectorvalued situation [9], where this explicit structure became more decisive. Here, it will be checked that these new operators are precisely the dyadic shifts in the generality defined by Lacey, Petermichl and Reguera [16]. Thus, closing the circle with the pioneering sharp estimates for the classical integral transforms, it is proven here that all Calderón-Zygmund operators may be written as averages of dyadic shifts (Theorem 4.2).…”
Section: Introductionmentioning
confidence: 72%
See 4 more Smart Citations
“…These auxiliary operators are already implicit in the original Nazarov-Treil-Volberg argument [22], and their more explicit form was identified in my extension of their result to the vectorvalued situation [9], where this explicit structure became more decisive. Here, it will be checked that these new operators are precisely the dyadic shifts in the generality defined by Lacey, Petermichl and Reguera [16]. Thus, closing the circle with the pioneering sharp estimates for the classical integral transforms, it is proven here that all Calderón-Zygmund operators may be written as averages of dyadic shifts (Theorem 4.2).…”
Section: Introductionmentioning
confidence: 72%
“…(3) A unified approach to the earlier results for B, H and R i was found by Lacey, Petermichl and Reguera [16], who proved (1.1) for a general class of "dyadic shifts," from which all the mentioned operators may be obtained by suitable averaging. The original proof employed a two-weight inequality for dyadic shifts due to Nazarov, Treil and Volberg [23].…”
Section: Introductionmentioning
confidence: 82%
See 3 more Smart Citations