Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $n$ linear embedding theorem   Let $\sigma_i$, $i=1,\ldots,n$, denote positive Borel measures on
$\mathbb{R}^d$, let $\mathcal{D}$ denote the usual collection of dyadic cubes
in $\mathbb{R}^d$ and let $K:\,\mathcal{D}\to[0,\infty)$ be a~map. In this
paper we give a~characterization of the $n$ linear embedding theorem. That is,
we give a~characterization of the inequality $$ \sum_{Q\in\mathcal{D}}
K(Q)\prod_{i=1}^n\left|\int_{Q}f_i\,d\sigma_i\right| \le C \prod_{i=1}^n
\|f_i\|_{L^{p_i}(d\sigma_i)} $$ in terms of multilinear Sawyer's checking
condition and discrete multinonlinear Wolff's potential, when $1<p_i<\infty$.

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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: cs