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29 March 2024
 
  » arxiv » 1104.4893

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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
AbstractWe 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
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