An estimate for multivariate interpolation II

Suppose u is a function on a domain Ω in all of whose mth order distributional derivatives are in L^p(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 l^p we obtain an estimate of the L^p(Ω) norm of u in terms of the l^p norm of these values and the L^p norms of its mth order derivatives. This result is useful in obtaining error estimates for certain interpolation schemes.