An Embedding Norm and the Lindqvist Trigonometric Functions
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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 .
CitationBennewitz, C., & Saito, Y. (2002). An embedding norm and the Lindqvist trigonometric functions. Electronic Journal of Differential Equations, 2002(86), pp. 1-6.
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