Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A sharp weighted Wirtinger inequality   We obtain a sharp estimate for the best constant $C>0$ in the Wirtinger type
inequality \[ \int_0^{2\pi}\gamma^pw^2\le C\int_0^{2\pi}\gamma^qw'^2 \] where
$\gamma$ is bounded above and below away from zero, $w$ is $2\pi$-periodic and
such that $\int_0^{2\pi}\gamma^pw=0$, and $p+q\ge0$. Our result generalizes an
inequality of Piccinini and Spagnolo.

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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: physics