Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operator-valued dyadic BMO spaces   We consider BMO spaces of operator-valued functions, among them the space of
operator-valued functions $B$ which define a bounded paraproduct on $L^2(H)$.
We obtain several equivalent formulations of $\|\pi_B\|$ in terms of the norm
of the "sweep" function of $B$ or of averages of the norms of martingales
transforms of $B$ in related spaces. Furthermore, we investigate a connection
between John-Nirenberg type inequalities and Carleson-type inequalities via a
product formula for paraproducts and deduce sharp dimensional estimates for
John-Nirenberg type inequalities.

15
The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga