Sharp Estimates of the Norms of Embeddings between Besov Spaces

Abstract

Optimal estimates are obtained for the rates of blow up of the norm of the embedding $B_{p,r}^s\hookrightarrow B_{q,r}^{s-n(\frac{1}{p}-\frac{1}{q})}$ with $p<q$ as $s\to n(\frac{1}{p}-\frac{1}{q})+$. We also show optimal limiting embeddings between Besov spaces and Lipschitz spaces.