Geodesic
An embedding norm and the Lindqvist trigonometric functions
Electronic journal of differential equations, Tome 2002 (2002)
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 
@article{EJDE_2002__2002__a208,
     author = {Bennewitz,  Christer and Sait\={o},  Yoshimi},
     title = {An embedding norm and the {Lindqvist} trigonometric functions},
     journal = {Electronic journal of differential equations},
     year = {2002},
     volume = {2002},
     zbl = {1015.46016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a208/}
}
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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__a208/