Note about non-compact embeddings between Besov spaces

Abstract: In this note, we look at the behavior of embedding between Besov spaces and compare its behavior with Sobolev embeddings, mainly when the embeddings are non-compact. We classify that in the case of the non-compact embedding then, depending on parameters, whether or not the embedding is finitely strictly singular and strictly singular. These results could be considered as a continuation and extension of recent results on non-compact "optimal" Sobolev embeddings.