On estimates for the uniform norm of the Laplace operator of the best interpolants on a class of bounded interpolation data

We consider an interpolation problem with minimum value of the uniform norm of the Laplace operator of interpolants for a class of bounded interpolated sequences. The data are interpolated at nodes of the grid formed by points from $\mathbb{R}^2$ with integer coordinates. Two-sided estimates for the uniform norm of the best interpolant are found, which improve known estimates.