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 $B_{p,\theta }^r$ 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 $B_{p,\theta }^r$ as well as on the Sobolev classes $W_{p,\mathbf{\alpha }}^r$ in the space $B_{\infty ,1}$ in the case $1\le p\le \infty$.