The isomorphic classification of Besov spaces over Rd revisited

Abstract

We take advantage of the recent developments in the isomorphic classification of the infinite matrix spaces of mixed norms ${\ell }_q\left({\ell }_p\right)$ for the whole range of values $0<p,q\le \infty$ to give a unified approach to the classification of Besov spaces over Euclidean spaces. In particular, we show that different Besov spaces with generalized smoothness ${\mathring{\mathrm{B}}}_{p,q}^w\left({\mathbb{R}}^d\right)$ over the Euclidean space ${\mathbb{R}}^d$ are isomorphic if and only if the indices $p$ and $q$ match.