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arXiv · 1106.1342

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

Fedor Nazarov·Alexander Reznikov·Alexander Volberg
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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 [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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Fedor Nazarov, Alexander Reznikov, Alexander Volberg. 2013-01-10. The proof of $A_2$ conjecture in a geometrically doubling metric space. https://arxiv.org/abs/1106.1342

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