Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Perfect Local $ Tb$ Theorem and Twisted Martingale Transforms   A local Tb Theorem provides a flexible framework for proving the boundedness
of a Calder\'on-Zygmund operator T. One needs only boundedness of the operator
T on systems of locally pseudo-accretive functions \{b_Q\}, indexed by cubes.
We give a new proof of this Theorem in the setting of perfect (dyadic) models
of Calder\'on-Zygmund operators, imposing integrability conditions on the b_Q
functions that are the weakest possible. The proof is a simple direct argument,
based upon a new inequality for transforms of so-called twisted martingale
differences.

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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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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: ao-sci
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The categories of this paper are: solv-int