Representation and m-term approximation for anisotropic Besov classes

In this paper, we discuss the best m-term approximation for the anisotropic Besov class of multivariate periodic functions. First we give the representation theorem of the anisotropic Besov class Bp,θr, then we study the best m-term approximation with respect to orthogonal dictionaries Ud. Moreover, it is established that the asymptotic order of the best m-term approximation can be achieved by a simply greedy algorithm.