Estimates of the characteristics of nonlinear approximation of classes of periodic functions of many variables

In the paper, we obtained exact order estimates of the best m-term trigonometric approximation and the best orthogonal trigonometric approximation of functions from the Nikol'skii-Besov Bʳp,θ(Tᵈ) and Sobolev Wʳp,α(Tᵈ) classes in the Lebesque subspaces Bq,1(Tᵈ) for some relations between the parameters p and q. The received results yield that estimates of the considered approximation characteristics in the multivariate case, in contrast to the univariate, in the spaces Bq,1(Tᵈ) and Lq(Tᵈ) differ in order. Besides, for some parameter values the obtained exact order estimates of the best m-term trigonometric approximation and the best orthogonal trigonometric approximation in the spaces Bq,1(Tᵈ) still remain unknown for the Lq(Tᵈ)-space.