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Article overview
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A simple sharp weighted estimate of the dyadic shifts on metric spaces with geometric doubling | Fedor Nazarov
; Alexander Volberg
; | Date: |
26 Apr 2011 | Abstract: | We give a short and simple polynomial estimate of the norm of weighted dyadic
shift on metric space with geometric doubling, which is linear in the norm of
the weight. Combined with the existence of special probability space of dyadic
lattices built in Reznikov--Volberg’s note "Random "dyadic" lattice in
geometrically doubling metric space and $A_2$ conjecture", Preprint arXiv:
1103.5246, and with decomposition of Calder’on--Zygmund operators to dyadic
shifts from T. Hyt"{o}nen, "Nonhomogeneous vector $Tb$ theorem", Preprint
arXiv:0809.3097 (and later T. Hyt"onen, C. P’erez, S. Treil, A. Volberg, "A
sharp estimated of weighted dyadic shifts that gives the proof of $A_2$
conjecture", Preprint arXiv 1010.0755), we will be able to have a linear (in
the norm of weight) estimate of an arbitrary Calder’on--Zygmund operator on a
metric space with geometric doubling. This will be published separately. | Source: | arXiv, 1104.4893 | Services: | Forum | Review | PDF | Favorites |
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