A sharp weighted Wirtinger inequality

Tonia Ricciardi

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A sharp weighted Wirtinger inequality

Tonia Ricciardi

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Abstract

We obtain a sharp estimate for the best constant $C>0$ in the Wirtinger type inequality \[ \int_0^{2π}γ^pw^2\le C\int_0^{2π}γ^qw'^2 \] where $γ$ is bounded above and below away from zero, $w$ is $2π$-periodic and such that $\int_0^{2π}γ^pw=0$, and $p+q\ge0$. Our result generalizes an inequality of Piccinini and Spagnolo.

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Tonia Ricciardi. 2005-01-04. A sharp weighted Wirtinger inequality. https://arxiv.org/abs/math/0501044

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