Representation and -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 B p , θ r , then we study the best m -term approximation with respect to orthogonal dictionaries U d . Moreover, it is established that the asymptotic order of the best m -term approximation can be achieved by a simply greedy algorithm.