Constructive sparse trigonometric approximations of functions with small mixed smoothness

Exact order bounds are obtained for the best $m$-term trigonometric approximation (in the integral metric) of periodic functions with small mixed smoothness from classes close to Nikol'skii-Besov type classes. The obtained bounds differ (under identical constraints on the smoothness) from the corresponding bounds of the best $m$-term trigonometric approximation of Besov classes of mixed smoothness established by A.S. Romanyuk. The upper bound is realized by a constructive method based on a greedy algorithm.