Widths and entropy numbers of the classes of periodic functions of one and several variables in the space $B_{q,1}$

Abstract

Exact-order estimates are obtained for the entropy numbers and several types of widths (Kolmogorov, linear, trigonometric and orthowidth) for the Sobolev and Nikol'skii-Besov classes of one and several variables in the space $B_{q,1}$, $1 <q< \infty$. It is shown, that in the multivariate case, in contrast to the univariate, the obtained estimates differ in order from the corresponding estimates in the space $L_q$.