Geodesic
An embedding norm and the Lindqvist trigonometric functions
Electronic Journal of Differential Equations, Tome 2002 (2002).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We shall calculate the operator norm $\|T\|_p$ of the Hardy operator $Tf = \int_0^x f $, where $1\le p\le \infty$. This operator is related to the Sobolev embedding operator from $W^{1,p}(0,1)/\mathbb{C}$ into $W^p(0,1)/\mathbb{C}$. For $1$, the extremal, whose norm gives the operator norm $\|T\|_p$, is expressed in terms of the function $\sin_p$ which is a generalization of the usual sine function and was introduced by Lindqvist [6].
Classification : 46E35, 33D05
Keywords: Sobolev embedding operator, Volterra operator 
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     title = {An embedding norm and the {Lindqvist} trigonometric functions},
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Bennewitz, Christer; Saitō, Yoshimi. An embedding norm and the Lindqvist trigonometric functions. Electronic Journal of Differential Equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a8/