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Article overview
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The proof of $A_2$ conjecture in a geometrically doubling metric space | | Fedor Nazarov
; Alexander Reznikov
; Alexander Volberg
; | | Date: |
7 Jun 2011 | | Abstract: | We give a proof of the $A_2$ conjecture in geometrically doubling metric
spaces (GDMS), i.e. a metric space where one can fit not more than a fixed
amount of disjoint balls of radius $r$ in a ball of radius $2r$. Our proof
consists of three main parts: a construction of a random "dyadic" lattice in a
metric space; a clever averaging trick from cite{Hyt}, which decomposes a
"hard" part of a Calderon-Zygmund operator into dyadic shifts (adjusted to
metric setting); and the estimates for these dyadic shifts, made in cite{NV}
and later in cite{Tr} | | Source: | arXiv, 1106.1342 | | Services: | Forum | Review | PDF | Favorites | |
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