Order estimates of the best $n$-term orthogonal trigonometric approximations of the classes ${\cal F}_{q}^{\psi}$ of periodic functions in the integral metrics

Abstract

We obtain order estimates in the spaces $L_p$ of the best $n$-term trigonometric orthogonal approximations of the classes ${\cal F}_{q}^{\psi}$ of periodic functions, whose Fourier coefficients decrease faster then any power function. We also obtain order estimates of the quantities of approximations by $n$-term Greedy approximants of such classes in the spaces $L_p$.