An embedding norm and the lindqvist trigonometric functions

Academic Article

Abstract

  • We shall calculate the operator norm ∥T∥p of the Hardy operator Tf = ∫0x f, where 1 ≤ p ≤ ∞. This operator is related to the Sobolev embedding operator from W1,p(0, 1)/ℂ into Wp(0, 1)/ℂ. For 1 < p < ∞, the extremal, whose norm gives the operator norm ∥T∥p, is expressed in terms of the function sinp which is a generalization of the usual sine function and was introduced by Lindqvist [6]. © 2002 Southwest Texas State University.
  • Authors

    Pubmed Id

  • 8294693
  • Author List

  • Bennewitz C; Saito Y
  • Volume

  • 2002