A sharp weighted Wirtinger inequality

Ricciardi, Tonia. "A sharp weighted Wirtinger inequality." Bollettino dell'Unione Matematica Italiana 8-B.1 (2005): 259-267. <http://eudml.org/doc/195264>.

@article{Ricciardi2005,
abstract = {We obtain a sharp estimate for the best constant $C>0$ in the Wirtinger type inequality $$ \int\_\{0\}^\{2\pi\}\gamma^\{p\}\omega^\{2\}\leq C \int\_\{0\}^\{2\pi\}\gamma^\{q\}\omega'^\{2\} $$ where $\gamma$ is bounded above and below away from zero, $w$ is $2\pi$-periodic and such that $\int_\{0\}^\{2\pi\}\gamma^\{p\}\omega=0$, and $p+q\geq 0$. Our result generalizes an inequality of Piccinini and Spagnolo.},
author = {Ricciardi, Tonia},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {259-267},
publisher = {Unione Matematica Italiana},
title = {A sharp weighted Wirtinger inequality},
url = {http://eudml.org/doc/195264},
volume = {8-B},
year = {2005},
}

TY - JOUR
AU - Ricciardi, Tonia
TI - A sharp weighted Wirtinger inequality
JO - Bollettino dell'Unione Matematica Italiana
DA - 2005/2//
PB - Unione Matematica Italiana
VL - 8-B
IS - 1
SP - 259
EP - 267
AB - We obtain a sharp estimate for the best constant $C>0$ in the Wirtinger type inequality $$ \int_{0}^{2\pi}\gamma^{p}\omega^{2}\leq C \int_{0}^{2\pi}\gamma^{q}\omega'^{2} $$ where $\gamma$ is bounded above and below away from zero, $w$ is $2\pi$-periodic and such that $\int_{0}^{2\pi}\gamma^{p}\omega=0$, and $p+q\geq 0$. Our result generalizes an inequality of Piccinini and Spagnolo.
LA - eng
UR - http://eudml.org/doc/195264
ER -