Estimates for the entropy numbers of the Nikol'skii-Besov classes of periodic functions of many variables in the space of quasi-continuous functions

TL;DR

This paper provides precise estimates for the entropy numbers of Nikol'skii-Besov classes of multivariable periodic functions within the space of quasi-continuous functions, advancing understanding of their compactness properties.

Contribution

It delivers exact-order estimates for the entropy numbers of Nikol'skii-Besov classes in the space of quasi-continuous functions, a novel result in this area.

Findings

Exact-order estimates for entropy numbers obtained

Results apply to multivariable periodic functions

Advances understanding of function class compactness

Abstract

We obtained exact-order estimates for the entropy numbers of the Nikol'skii-Besov classes $B^{\boldsymbol{r}}_{p,\theta}$ of periodic functions of many variables in the metric of the space of quasi-continuous functions.