Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conditioned square functions for noncommutative martingales   We prove a weak-type (1, 1) inequality involving conditioned versions of
square functions for martingales in noncommutative $L^p$-spaces associated with
finite von Neumann algebras. As application, we determine the optimal orders
for the best constants in the noncommutative Burkholder/Rosenthal inequalities
from [Ann. Probab. 31 (2003) 948--995]. We also discuss BMO-norms of sums of
noncommuting order-independent operators.

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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph