Sharp interpolation inequalities for discrete operators and applications

Abstract

We consider interpolation inequalities for imbeddings of the l 2 -sequence spaces over d-dimensional lattices into the l ∞ 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.