Kolmogorov Numbers of Embeddings of Besov Spaces of Dominating Mixed Smoothness into $L_{\infty}$

TL;DR

This paper provides precise estimates of Kolmogorov numbers for embeddings of Besov spaces with dominating mixed smoothness into the space of essentially bounded functions, advancing understanding of their compactness properties.

Contribution

It offers two-sided sharp estimates for Kolmogorov numbers of these embeddings, which was previously unexplored or incomplete.

Findings

Sharp two-sided estimates obtained

Enhanced understanding of embedding compactness

Contributes to approximation theory in functional analysis

Abstract

In this paper we shall give two-sided sharp estimates of Kolmogorov numbers of embeddings of the Besov spaces with dominating mixed smoothness $S^t_{p,q}B((0,1)^d)$ into $ L_{\infty}((0,1)^d)$.