Pointwise approximation with quasi-interpolation by radial basis functions

We consider radial basis function approximations using at first a localization of the basis functions known as quasi-interpolation (to be contrasted to the plain linear combinations of shifts of radial basis functions or for instance cardinal interpolation). Using these quasi-interpolants we derive various pointwise error estimates in LpLp for p∈[1,∞)p∈[1,∞).