An improved order of approximation for thin-plate spline interpolation in the unit disc

We show that the L-p-norm of the error in thin-plate spline interpolation i n the unit disc decays like O(h(gamma p+1/2)), where gamma(p) := min{2, 1 2/p}, under the assumptions that the function to be approximated is C-infi nity and that the interpolation points contain the finite grid {hj : j is a n element of Z(2), \hj\ < 1 - h}.