On derivatives of complex order in some weighted Banach spaces and interpolation. (English) Zbl 1292.46012
Summary: The notion of complex derivatives is used to prove interpolation theorems mainly in weighted Banach spaces. A conjecture of M. Artola [in: Équations aux dérivées partielles et applications. Articles dédiés à Jacques-Louis Lions. Gauthier-Villars: Paris. 35–50 (1998; Zbl 0920.46026)] concerning the weights is solved and a characterization is given.
MSC:
| 46B70 | Interpolation between normed linear spaces |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
