Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A characterization of product BMO by commutators   Let b be a function on the plane. Let H_j, j=1,2, be the Hilbert transform
acting on the j-th coordinate on the plane. We show that the operator norm of
the double commutator [[ M_b, H_1], H_2] is equivalent to the Chang-Fefferman
BMO norm of b. Here, M_b denotes the operator which is multiplication by b.
  This result extends a well known theorem of Nehari on weak factorization in
the Hardy space H^1 to the same theorem on H^1 of a product domain. The product
setting is more delicate because of the presence of a two parameter family of
dilations. The method of proof depends upon (a) A dyadic decomposition of
product BMO by wavelets (b) a prior estimate of Ferguson and Sadosky involving
rectangular BMO (c) and a careful control of certain measures related to those
of Carleson.

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The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics