Bernstein Numbers of Embeddings of Isotropic and Dominating Mixed Besov Spaces

TL;DR

This paper studies the decay rates of Bernstein numbers for embeddings of isotropic and dominating mixed Besov spaces into Lebesgue spaces, providing insights into their asymptotic behavior.

Contribution

It offers a detailed analysis of Bernstein numbers for specific Besov space embeddings, including asymptotic decay rates, which were previously less understood.

Findings

Decay rates of Bernstein numbers characterized

Asymptotic behavior of identity embeddings analyzed

Results applicable to isotropic and mixed Besov spaces

Abstract

The purpose of the present paper is to investigate the decay of Bernstein numbers of the embedding from $B^t_{p_1,q}((0,1)^d)$ into the space $L_{p_2}((0,1)^d) $. The asymptotic behaviour of Bernstein numbers of the identity $id: S_{p_1,p_1}^tB((0,1)^d)\rightarrow L_{p_2}((0,1)^d)$ will be also considered.