The best $m$-term trigonometric approximations of the classes of periodic functions of one and many variables in the space $B_{q,1}$

Abstract

Exact order estimates are obtained of the best $m$-term trigonometric approximations of the Nikol'skii-Besov classes $B^r_{p, \theta}$ of periodic functions of one and many variables in the space $B_{q,1}$. In the univariate case ($d=1$), we get the orders of the respective approximation characteristics on the classes $B^r_{p, \theta}$ as well as on the Sobolev classes $W^r_{p, {\boldsymbol{\alpha}}}$ in the space $B_{\infty,1}$ in the case $1\leqslant p \leqslant \infty$.

Keywords

• nikol'skii-besov classes
• sobolev classes
• best m-term trigonometric approximation