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.

Rights

Attribution 4.0 International

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