Weyl and Bernstein Numbers of Embeddings of Sobolev Spaces with Dominating Mixed Smoothness

TL;DR

This paper investigates the asymptotic behavior of Weyl and Bernstein numbers for embeddings of Sobolev spaces with dominating mixed smoothness into Lebesgue spaces, extending previous research in this area.

Contribution

It provides new asymptotic estimates for Weyl and Bernstein numbers of these embeddings, advancing understanding of their compactness properties.

Findings

Asymptotic behavior characterized for Weyl numbers

Asymptotic behavior characterized for Bernstein numbers

Extension of previous results on Sobolev space embeddings

Abstract

This paper is a continuation of the papers [21] and [22]. Here we shall investigate the asymptotic behaviour of Weyl and Bernstein numbers of embeddings of Sobolev spaces with dominating mixed smoothness into Lebesgue spaces.