On the vanishing of cohomology groups with values in a product sheaf.
We prove that no ultraproduct of Banach spaces via a countably incomplete ultrafilter can contain c₀ complemented. This shows that a "result" widely used in the theory of ultraproducts is wrong. We then amend a number of results whose proofs have been infected by that statement. In particular we provide proofs for the following statements: (i) All M-spaces, in particular all C(K)-spaces, have ultrapowers isomorphic to ultrapowers of c₀, as also do all their complemented subspaces isomorphic to their...
Nous établissons des résultats d’interpolation non-standards entre les espaces de Besov et les espaces et , avec des applications aux lemmes de régularité en moyenne et aux inégalités de type Gagliardo-Nirenberg. La preuve de ces résultats utilise les décompositions dans des bases d’ondelettes.