Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The One-Third-Trick and Shift Operators   In this paper we obtain a representation as martingale transform operators
for the rearrangement and shift operators introduced by T. Figiel. The
martingale transforms and the underlying sigma algebras are obtained explicitly
by combinatorial means. The known norm estimates for those operators are a
direct consequence of our representation.

15
The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
1
The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex