Abstract
Order-sharp estimates are established for the best N-term approximations of functions in the classes $$B_{pq}^{sm} (\mathbb{T}^k )$$ and $$L_{pq}^{sm} (\mathbb{T}^k )$$ of Nikol’skii-Besov and Lizorkin-Triebel types with respect to the multiple system of Meyer wavelets in the metric of $$L_r (\mathbb{T}^k )$$ for various relations between the parameters s, p, q, r, and m (s = (s 1, ..., s n ) ∈ ℝ + , 1 ≤ p, q, r ≤ ∞, m = (m 1, ..., m n ) ∈ ℕ n , and k = m 1 + ... + m n ). The proof of upper estimates is based on variants of the so-called greedy algorithms.