Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two weight $L^p$ estimates for paraproducts in non-homogeneous settings   We give a necessary and sufficient condition for the two weight
$L^p$-estimates for paraproducts in non-homogeneous settings, $1<p<\infty$. We
are mainly interested in the case $p\ne 2$, since the case $p=2$ is a
well-known and easy corollary of the Carleson embedding theorem. The necessary
and sufficient condition is given in terms of testing conditions of Sawyer
type: for $p\le 2$ only one ("direct") testing condition is required, but for
$p>2$ both "direct" and "adjoint" testing conditions are needed. An interesting
feature is that the "adjoint" testing condition is that it is a testing
condition not for the adjoint of the paraproduct, but for some auxiliary
operator.

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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys