Widths of embeddings of 2-microlocal Besov spaces

TL;DR

This paper investigates the asymptotic properties of various approximation numbers for compact embeddings between 2-microlocal Besov spaces, providing sharp estimates including in quasi-Banach settings.

Contribution

It offers new sharp asymptotic estimates for approximation, Gelfand, and Kolmogorov numbers of embeddings between 2-microlocal Besov spaces, extending results to quasi-Banach spaces.

Findings

Sharp asymptotic estimates for approximation numbers

Results include quasi-Banach space settings

Detailed analysis of embeddings related to d-sets

Abstract

We consider the asymptotic behaviour of the approximation, Gelfand and Kolmogorov numbers of compact embeddings between 2-microlocal Besov spaces with weights defined in terms of the distance to a $d$-set $U\subset \mathbb{R}^n$. The sharp estimates are shown in most cases, where the quasi-Banach setting is included.