Generalized Lions-Peetre interpolation construction and optimal embedding theorems for Sobolev spaces. (English, Russian) Zbl 1316.46022
Sb. Math. 205, No. 1, 83-100 (2014); translation from Mat. Sb. 205, No. 1, 101-155 (2014).
Summary: In the paper, a new description of the generalized Lions-Peetre method of means is found, which enables one to evaluate the interpolation orbits of spaces constructed by this method. The list of these spaces includes all Lorentz spaces with functional parameters, Orlicz spaces, and spaces close to them. This leads in turn to new optimal embedding theorems for Sobolev spaces produced using the Lions-Peetre construction in rearrangement invariant spaces. It turns out that the optimal space of the embedding is also a generalized Lions-Peetre space whose parameters are explicitly evaluated.
MSC:
| 46B70 | Interpolation between normed linear spaces |
| 46M35 | Abstract interpolation of topological vector spaces |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
