Electron. J. Diff. Eqns., Vol. 2002(2002), No. 86, pp. 1-6.
### An embedding norm and the Lindqvist trigonometric functions

Christer Bennewitz & Yoshimi Saito

**Abstract:**

We shall calculate the operator norm
of the Hardy operator

,
where
.

This operator is related to the Sobolev embedding operator from
into
.
For
,
the extremal, whose norm gives the operator norm
,
is expressed in terms of the function
which is a generalization of the usual sine function and
was introduced by Lindqvist [6].
Submitted September 12, 2002. Published October 9, 2002.

Math Subject Classifications: 46E35, 33D05.

Key Words: Sobolev embedding operator, Volterra operator.

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Christer Bennewitz

Department of Mathematics, Lund University,

Box 118,22100 Sweden

e-mail: christer.bennewitz@math.lu.se
Yoshimi Saito

Dept. of Mathematics, University of Alabama at Birmingham,

Birmingham, AL 35294, USA.

e-mail: saito@math.uab.edu

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