Geodesic
Generalized Lions-Peetre interpolation construction and optimal embedding theorems for Sobolev spaces
Sbornik. Mathematics, Tome 205 (2014) no. 1, pp. 83-100

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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. Bibliography: 18 titles.
Keywords: embedding theorems, rearrangement invariant spaces, generalized Lions-Peetre spaces of means.
Mots-clés : Sobolev spaces, interpolation orbits 
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     author = {V. I. Ovchinnikov},
     title = {Generalized {Lions-Peetre} interpolation construction and optimal embedding theorems for {Sobolev} spaces},
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V. I. Ovchinnikov. Generalized Lions-Peetre interpolation construction and optimal embedding theorems for Sobolev spaces. Sbornik. Mathematics, Tome 205 (2014) no. 1, pp. 83-100. http://geodesic.mathdoc.fr/item/SM_2014_205_1_a4/