TY - JOUR AU - A. S. Romanyuk PY - 2015/11/25 Y2 - 2024/03/29 TI - Estimation of the Entropy Numbers and Kolmogorov Widths for the Nikol’skii–Besov Classes of Periodic Functions of Many Variables JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 67 IS - 11 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2088 AB - We establish order estimates for the entropy numbers of the Nikol’skii–Besov classes $B_{p,θ}^r$ of periodic functions of many variables in the space $L_q$ with certain relations between the parameters $p$ and $q$. By using the obtained lower estimates of the entropy numbers, we establish the exact-order estimates for the Kolmogorov widths of the same classes of functions in the space $L_1$. ER -