Estimates for the entropy numbers of the classes $B_{p,θ}^{Ω}$ of periodic multivariate functions in the uniform metric

Abstract

We establish order estimates for the entropy numbers of the classes $B_{p,θ}^{Ω}$ of periodic multivariate functions in the uniform metric. For the proper choice of the functions $\Omega$, these classes coincide with the Nikol’skii – Besov classes $B_{p,θ}^{r}$.