Greedy algorithm with regard to the needlet system on the sphere

Order estimates of the best m-term approximation for the Besov classes and the Sobolev classes with regard to the dictionary Ψ on the sphere are established, where Ψ consists of needlets which are highly localized radial polynomials on the sphere with centers at the nodes of a suitable cubature rule. Moreover, it is shown that for these classes the orders of the best m-term approximation can be achieved by simple greedy type algorithm.