The Proof of A_2 Conjecture in a Geometrically Doubling Metric Space

摘要

We give a proof of the A2 conjecture in geometrically doubling metric spaces (GDMS), that is, a metric space where one can fit no 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 Calderón-Zygmund operator into dyadic shifts (adjusted to metric setting); and the estimates for these dyadic shifts, made in [16] and later in [19].