Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bilinear Rubio de Francia inequalities for collections of non-smooth
  squares   Let $\Omega$ be a collection of disjoint dyadic squares $\omega$, let
$\pi_\omega$ denote the non-smooth bilinear projection onto $\omega$ \[
\pi_\omega (f,g)(x):=\int\int \mathbf{1}_{\omega}(\xi,\eta) \widehat{f}(\xi)
\widehat{g}(\eta) e^{2\pi i (\xi + \eta) x} d \xi d\eta \] and let $r>2$. We
show that the bilinear Rubio de Francia operator \[ \Big(\sum_{\omega\in\Omega}
|\pi_{\omega} (f,g)|^r \Big)^{1/r} \] is $L^p \times L^q \rightarrow L^s$
bounded with constant independent of $\Omega$ whenever $1/p + 1/q = 1/s$,
$r'<p,q<r$, $r'/2 < s < r/2$.

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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: stat
12
The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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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: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom