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Sharp weighted estimates of the dyadic shifts and $A_2$ conjecture | | Tuomas Hytönen
; Carlos Pérez
; Sergei Treil
; Alexander Volberg
; | | Date: |
5 Oct 2010 | | Abstract: | Using the combination of three recent papers we give a direct and short proof
of $A_2$ conjecture, which claims that the norm of any Calder’on-Zygmund
operator is bounded by the first degree of the $A_2$ norm of the weight. These
three papers are:
a) T. Hyt"onen "The sharp weighted bound for general Calder’on-Zygmund
operators",
b) Nazarov-Treil-Volberg "Two weight inequalities for individual Haar
multipliers and other well localized operators",
and, finally,
c) Lacey-Petermichl-Reguera "Sharp $A_2$ inequality for Haar shift
operators".
The ingredients of the proof include:
a) a sharp two weight estimates for dyadic shifts,
b) a decomposition of an arbitrary Calder’on-Zygmund operator to the "sum"
of dyadic shifts and dyadic paraproducts.
The method of the proof amounts to the refinement of the techniques from
nonhomogeneous Harmonic Analysis. | | Source: | arXiv, 1010.0755 | | Services: | Forum | Review | PDF | Favorites | |
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