Nonlinear wavelet approximation in anisotropic Besov spaces

Given anisotropic: wavelet decompositions associated with the smoothness beta, beta = (beta(1), . . . , beta(d)), beta(1), . . . , beta(d) > 0 of multivariate functions as measured in anisotropic Besov spaces B-beta, we give the rate of nonlinear approximation with respect to the L-P-norm, 1 less than or equal to p < infinity, of functions f is an element of B-beta by these wavelets. We also prove that, among a general class of anisotropic wavelet decompositions of a function f is an element of B-beta the anisotropic wavelet decomposition associated with beta gives the optimal rate of compression of the wavelet decomposition of f.