We consider an interpolation problem with minimum value of the -norm (<) of the Laplace operator of interpolants for a class of interpolated sequences that are bounded in the -norm. The data are interpolated at nodes of the grid formed by points from with integer coordinates. It is proved that, if <, then the -norm of the Laplace operator of the interpolant can be arbitrarily small for any sequence that is interpolated. Two-sided estimates for the -norm of the Laplace operator of the best interpolant are found for the case .