Error estimates for scattered data interpolation on spheres

We study Sobolev type estimates for the approximation order resulting from using strictly positive definite kernels to do interpolation on the n-spher e. The interpolation knots are scattered. Our approach partly follows the g eneral theory of Golomb and Weinberger and related estimates. These error e stimates are then based on series expansions of smooth functions in terms o f spherical harmonics. The Markov inequality for spherical harmonics is ess ential to our analysis and is used in order to find lower bounds for certai n sampling operators on spaces of spherical harmonics.