Interpolation by functions from a Sobolev space with minimum L-p-norm of the Laplace operator

We consider an interpolation problem with minimum value of the L-p-norm (1 <= p < infinity) of the Laplace operator of interpolants for a class of interpolated sequences that are bounded in the l(p)-norm. The data are interpolated at nodes of the grid formed by points from R-n with integer coordinates. It is proved that, if 1 <= p < n/2, then the L-p-norm of the Laplace operator of the interpolant can be arbitrarily small for any sequence that is interpolated. Two-sided estimates for the L-2-norm of the Laplace operator of the best interpolant are found for the case n = 2.