Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A restricted weak type inequality with application to a Tp theorem and
  optimal cancellation conditions for CZO's   This paper continues the investigation begun in arXiv:1906.05602 of extending
the T1 theorem of David and Journ\'e, and optimal cancellation conditions, to
more general weight pairs. The main additional tool developed here is a two
weight restricted weak type inequality. Assuming {\sigma} and {\omega} are
locally finite positive Borel measures, with one of them an A infinity weight,
we show that the two weight restricted weak type inequality for an
{\alpha}-fractional Calder\'on-Zygmund singular integral T holds if and
(provided T is elliptic) only if the classical fractional Muckenhoupt condition
holds. In the case {\alpha} = 0, boundedness of T on unweighted L2 is assumed
as well. Applications are then given to a Tp theorem for CZO's with doubling
weights when one is A infinity, and then to optimal cancellation conditions for
CZO's in terms of polynomial testing in similar situations.

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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci