The proof of A₂ conjecture in a geometrically doubling metric space

2011/06/07 by Nazarov, Fedor, Reznikov, Alexander, Volberg, Alexander
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1106.1342

Abstract

We give a proof of the A₂ 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 [3], 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 [16] and later in [19].

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