The isomorphic classification of Besov spaces over \(\mathbb R^d\) revisited. (English) Zbl 1354.46034
Summary: We take advantage of the recent developments in the isomorphic classification of the infinite matrix spaces of mixed norms \(\ell_q(\ell_p)\) for the whole range of values \(0<p,q\leq\infty\) 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 \({\mathop{B}\limits^\circ}_{p,q}^w(\mathbb R^d)\) over the Euclidean space \(\mathbb R^d\) are isomorphic if and only if the indices \(p\) and \(q\) match.
MSC:
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 42B35 | Function spaces arising in harmonic analysis |
| 46B25 | Classical Banach spaces in the general theory |
| 46B03 | Isomorphic theory (including renorming) of Banach spaces |
| 46B45 | Banach sequence spaces |
Keywords:
Besov spaces (weighted); \(L_{p}\)-spaces; wavelets; sequence spaces; isomorphic classificationReferences:
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