Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positivity of $|p|^a|q|^b+|q|^b|p|^a$   We show that $$J_{a,b,n}:=\frac12(|p|^a|q|^b+|q|^b|p|^a)$$ is positive, if
$n\geq b+a$. (Here $q$ is the multiplication by $x$ and $p:=
\mathrm{i}^{-1}\nabla$.) Furthermore we show that it generalizes the
generalized Hardy inequalities for the fractional Laplacians.

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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: physics
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat