Best [formula omitted]-term trigonometric approximation of periodic functions of several variables from Nikol’skii–Besov classes for small smoothness

Abstract

We find the asymptotic orders of best m-term trigonometric approximation for Nikol’skii–Besov classes Bp,θr of periodic functions of several variables in the space Lq, 1≤p≤2<q<∞, for the cases of “small” smoothness dp−dq<r<dp and for the “critical” value of the smoothness r=dp. These results are complementary to the estimates of the best m-term trigonometric approximation for classes Bp,θr obtained by R.A. DeVore and V.N. Temlyakov.