  To improve convergence results obtained using a framework for unsymmetric
meshless methods due to Schaback (Preprint G\"ottingen 2006), we extend, in two
directions, the Sobolev bound due to Arcang\'eli et al. (Numer Math 107,
181-211, 2007), which itself extends two others due to Wendland and Rieger
(Numer Math 101, 643-662, 2005) and Madych (J. Approx Theory 142, 116-128,
2006). The first is to incorporate discrete samples of arbitrary order
derivatives into the bound, which are used to obtain higher order convergence
in higher order Sobolev norms. The second is to optimally bound fractional
order Sobolev semi-norms, which are used to obtain more optimal convergence
rates when solving problems requiring fractional order Sobolev spaces, notably
inhomogeneous boundary value problems.
