Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On $A_2$ conjecture and corona decomposition of weights   We consider here a problem of finding the sharp estimate for the boundedness
of an arbitrary Calder\'on-Zygmund operator in $L^2(w)$, $w\in A_2$. We first
prove that for $A_2$ weight $w$ one has that the norm a Calderon--Zygmund
operator $T$ in $L^2(w)$ is bounded by the sum of its weak norm, the weak norm
of its adjoint, and the $A_2$ norm of the weight. From this result we derive
that $\|T\|_{L^2(w)\rightarrow L^2(w)} \le C\,[w]_{A_2}\log (1+[w]_{A_2})$. We
believe that the logarithmic factor is superflous. The approach is based on
$2$-weight estimates technique and, hence, on non-homogeneous harmonic
analysis.

5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys