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arXiv · 1407.0675

Sharp interpolation inequalities for discrete operators and applications

Alexei Ilyin·Ari Laptev·Sergey Zelik
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Abstract

We consider interpolation inequalities for imbeddings of the $l^2$-sequence spaces over $d$-dimensional lattices into the $l^\infty_0$ spaces written as interpolation inequality between the $l^2$-norm of a sequence and its difference. A general method is developed for finding sharp constants, extremal elements and correction terms in this type of inequalities. Applications to Carlson's inequalities and spectral theory of discrete operators are given.

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Alexei Ilyin, Ari Laptev, Sergey Zelik. 2014-07-02. Sharp interpolation inequalities for discrete operators and applications. https://arxiv.org/abs/1407.0675

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