Optimal recovery of Besov classes of generalized smoothness and Sobolev classes on the sphere

We want to recover continuous functions on the sphere Sd−1Sd−1 using only their function values. We obtain the asymptotic orders of the sampling numbers and the linear sampling numbers of Besov classes BBp,θΩ(Sd−1) of generalized smoothness and the Sobolev classes BWpr(Sd−1) in Lq(Sd−1)Lq(Sd−1) for all 1≤p,q,θ≤∞1≤p,q,θ≤∞.