  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.
