AbstractSuppose u is a function on a domain Ω in Rn all of whose mth order distributional derivatives are in Lp(Ω) and m is sufficiently large to imply that u is continuous. If the values of u on a sufficiently dense, but not necessarily regular, grid of points are in lp we obtain an estimate of the Lp(Ω) norm of u in terms of the lp norm of these values and the Lp norms of its mth order derivatives. This result is useful in obtaining error estimates for certain interpolation schemes.