Estimation of the Entropy Numbers and Kolmogorov Widths for the Nikol’skii–Besov Classes of Periodic Functions of Many Variables

• Date: 2015
• Main Authors: Romanyuk, A. S., Романюк, А. С.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2015
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2088
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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-...