An estimate for multivariate interpolation II

  • Authors:

  • W. R. Madych

  • Affiliations:

  • Mathematics Department, University of Connecticut, Storrs, CT and Biomathematics Department of the GSF, Munich

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2006

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Abstract

Suppose 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.