Exact order estimates are obtained of the best m-term trigonometric approximations of the Nikol'skii-Besov classes B r p,θof periodic functions of one and many variables in the space B q,1 . In the univariate case (d = 1), we get the orders of the respective approximation characteristics on the classes B r p,θ as well as on the Sobolev classes W r p,α in the space B ∞,1 in the case 1 ≤ p ≤ ∞.

517.51Exact-order estimates are obtained for the best orthogonal trigonometric approximations of the Besov ( B p r , θ ) and Nukol'skii ( H p r ) classes of periodic functions of many variables in the metric of L q , 1 ≤ p, q ≤ ∞. We also establish the orders of the best approximations of functions from the same classes in the spaces L 1 and L ∞ by trigonometric polynomials with the corresponding spectrum.

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