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

Anatolii S. Romanyuk and Serhii Ya. Yanchenko

Mathematische Nachrichten, 2023, vol. 296, issue 6, 2575-2587

Abstract: We obtained order estimates for the entropy numbers of the Nikol'skii–Besov classes of functions Bp,θr(Td)$B^{\bm{r}}_{p,\theta }(\mathbb {T}^d)$ with mixed smoothness in the metric of the space of quasi‐continuous functions QC(Td)$QC(\mathbb {T}^d)$. We also showed that for 2≤p≤∞$2\le p \le \infty$, 2≤θ 12$r_1>\frac{1}{2}$, d≥2$d\ge 2$, the estimate of the corresponding asymptotic characteristic is exact in order.

Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.202100202

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:296:y:2023:i:6:p:2575-2587

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().