The proof of $A_2$ conjecture in a geometrically doubling metric space

Details The proof of $A_2$ conjecture in a geometrically doubling metric space The proof of $A_2$ conjecture in a geometrically doubling metric space

2011-06-07

arxiv.org/abs/1106.1342v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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}

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