The best M-term trigonometric approximations of the classes of periodic multivariate functions with bounded generalized derivative in the space Lq

摘要

The order estimates of the best M-term trigonometric approximations of functions Dβψ and the classes of (ψ,β)-differentiable periodic multivariate functions in the space Lq, 2 ≤ q ≤ ∞ are obtained. It is shown that, under certain conditions imposed on the parameter q, the best M-term trigonometric approximationsthave better order than the best orthogonal trigonometric approximations