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

Abstract

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

16 pages