An Embedding Norm and the Lindqvist Trigonometric Functions
Date
2002-10-09
Authors
Bennewitz, Christer
Saito, Yoshimi
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We shall calculate the operator norm ||T||p of the Hardy operator Tƒ = ∫x0 ƒ, 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 sin p which is a generalization of the usual sine function and was introduced by Lindqvist [6].
Description
Keywords
Sobolev embedding operator, Volterra operator
Citation
Bennewitz, C., & Saito, Y. (2002). An embedding norm and the Lindqvist trigonometric functions. <i>Electronic Journal of Differential Equations, 2002</i>(86), pp. 1-6.