We study the problem of estimating the $ p $ -norms ( $ 1\leq p\leq\infty $ ) of solutionsto inhomogeneous difference equations. The difference equations are consideredas bi-infinite (infinite in both directions) systems of linear equations. We establishestimates in the case of a diagonally dominant Laurent matrix.Using this resultand the idea of matrix decomposition into the product of matrices relatedto the decomposition of the characteristic polynomial,we propose some estimates in the caseof an arbitrary nonsingular band Laurent matrix.
