Christer Bennewitz & Yoshimi Saito
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 .
Submitted September 12, 2002. Published October 9, 2002.
Math Subject Classifications: 46E35, 33D05.
Key Words: Sobolev embedding operator, Volterra operator.
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Dept. of Mathematics, University of Alabama at Birmingham,
Birmingham, AL 35294, USA.