Embeddings of anisotropic Besov spaces into Sobolev spaces

TL;DR

This paper investigates how anisotropic Besov spaces, defined via an expansive matrix, embed into Sobolev spaces, providing precise conditions that depend on the matrix and parameters.

Contribution

It offers new sharp characterizations of embeddings for anisotropic Besov spaces into Sobolev spaces, highlighting the influence of the matrix on these embeddings.

Findings

Derived sharp embedding conditions for a wide parameter range

Identified the role of the expansive matrix in embedding behaviour

Extended understanding of anisotropic function space relationships

Abstract

We study the embeddings of (homogeneous and inhomogeneous) anisotropic Besov spaces associated to an expansive matrix $A$ into Sobolev spaces, with focus on the influence of $A$ on the embedding behaviour. For a large range of parameters, we derive sharp characterizations of embeddings.