Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Two Weight Inequality for Hilbert Transform, Coronas, and Energy
  Conditions   We consider the two weight problem for the Hilbert transform, namely the
question of finding real-variable characterization of those pair of weights for
which the Hilbert transform acts boundedly on $ L ^2 $ of the weights. Such a
characterization is known subject to certain side conditions. We give a new
proof, simpler in many details, of the best such result. In addition, we
analyze underlying assumptions in the proof, especially in terms of two
alternate side conditions. A new characterization in the case of one doubling
weight is given.

22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol