Estimates for the entropy numbers of the Nikol'skii–Besov classes of functions with mixed smoothness in the space of quasi‐continuous functions

Abstract

We obtained order estimates for the entropy numbers of the Nikol'skii-Besov classes of functions 𝐵 𝒓 𝑝,𝜃 (𝕋 𝑑 ) with mixed smoothness in the metric of the space of quasi-continuous functions 𝑄𝐶(𝕋 𝑑 ). We also showed that for, 𝑑 ≥ 2, the estimate of the corresponding asymptotic characteristic is exact in order.