Geodesic
The Wirtinger–Steklov inequality between the norm of a periodic function and the norm of the positive cutoff of its derivative
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 3, pp. 99-111 
E. A. Zernyshkina. The Wirtinger–Steklov inequality between the norm of a periodic function and the norm of the positive cutoff of its derivative. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 3, pp. 99-111. http://geodesic.mathdoc.fr/item/TIMM_2008_14_3_a8/
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     title = {The {Wirtinger{\textendash}Steklov} inequality between the norm of a~periodic function and the norm of the positive cutoff of its derivative},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We study the sharp constant in the inequality between the $L_p$-mean ($p\ge0$) of a $2\pi$-periodic function with zero mean value and the $L_q$-norm ($q\ge1$) of the positive cutoff of its derivative. We obtain estimates of the constant from below for $0\le p\le\infty$ and from above for $1\le p\le\infty$ for an arbitrary $1\le q\le\infty$. We write out the values of the sharp constant in the cases $p=2$, $1\le q\le\infty$ and $p=\infty$, $1\le q\le\infty$.

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