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We find the exact order estimates of the approximations of the classes ${\calF}_{q,r}^{\psi}$ of functions of several variables by greedy approximants inthe integral metric. We also obtain the exact order estimates of the best$n$-term orthogonal trigonometric approximations of the classes ${\calF}_{q,r}^{\psi}$ in the integral metric.

Approximations of certain classes of functions of several variables by greedy approximants in the integral metrics