Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An operator-valued $T1$ theory for symmetric CZOs   We provide a natural BMO-criterion for the $L_2$-boundedness of
Calder\'on-Zygmund operators with operator-valued kernels satisfying a
symmetric property. Our arguments involve both classical and quantum
probability theory. In the appendix, we give a proof of the $L_2$-boundedness
of the commutators $[R_j,b]$ whenever $b$ belongs to the Bourgain's
vector-valued BMO space, where $R_j$ is the $j$-th Riesz transform. A common
ingredient is the operator-valued Haar multiplier studied by Blasco and Pott.

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The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ