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 Carlsons inequalities and spectral theory of discrete operators are given.
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