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april 2010 A sharp weighted Wirtinger inequality and some related functional spaces
Raffaella Giova, Tonia Ricciardi
Bull. Belg. Math. Soc. Simon Stevin 17(2): 209-218 (april 2010). DOI: 10.36045/bbms/1274896200

Abstract

We consider the generalized Wirtinger inequality \[ \left( \int_{0}^{T} a |u|^q \right)^{1/q} \le C \biggm(\int_{0}^{T} a^{1-p} |u'|^{p}\biggm)^{1/p}, \] with $p,q>1$, $T>0$, $a\in L^1[0,T]$, $a\ge0$, $a\not\equiv0$ and where $u$ is a $T$-periodic function satisfying the constraint \[ \int_{0}^{T} a |u|^{q-2}u =0. \] We provide the best constant $C>0$ as well as all extremals. Furthermore, we characterize the natural functional space where the inequality is defined.

Citation

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Raffaella Giova. Tonia Ricciardi. "A sharp weighted Wirtinger inequality and some related functional spaces." Bull. Belg. Math. Soc. Simon Stevin 17 (2) 209 - 218, april 2010. https://doi.org/10.36045/bbms/1274896200

Information

Published: april 2010
First available in Project Euclid: 26 May 2010

zbMATH: 05735929
MathSciNet: MR2663466
Digital Object Identifier: 10.36045/bbms/1274896200

Subjects:
Primary: 26D15

Rights: Copyright © 2010 The Belgian Mathematical Society

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Vol.17 • No. 2 • april 2010
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