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

Sharp interpolation inequalities for discrete operators and applications