Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two Weight Inequality for the Hilbert Transform: A Real Variable
  Characterization, I   The two weight inequality for the Hilbert transform arises in the settings of
analytic function spaces, operator theory, and spectral theory, and what would
be most useful is a characterization in the simplest real-variable terms. We
show that the $L^2$ to $L^2$ inequality holds if and only if two L^2 to
weak-L^2 inequalities hold. This is a corollary to a characterization in terms
of a two-weight Poisson inequality, and a pair of testing inequalities on
bounded functions.

18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph