Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The proof of $A_2$ conjecture in a geometrically doubling metric space   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].

32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th