Geodesic
On the interpolation properties of certain quasilinearizable pairs
Sbornik. Mathematics, Tome 189 (1998) no. 2, pp. 227-234

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For a quasilinearizable pair of reflexive spaces $\{A_0,A_1\}$, the interpolation properties of the derived pair $\{A_0+A_1,\ A_0\cap A_1\}$ are studied. A real interpolation formula is proved that connects the interpolation spaces of the pairs $\{A_0,A_1\}$ and $\{A_0+A_1,A_0\cap A_1\}$. In particular, it turns out that the corresponding interpolation spaces coincide for $\theta =\frac 12$. The results are applied to generalized Nikol'skii-Besov spaces (the quasilinearizability of a pair $\bigl \{B_{p,q}^1(\mu _0),B_{p,q}^1(\mu _1)\bigr \}$ of such spaces is proved beforehand). 
@article{SM_1998_189_2_a1,
     author = {A. G. Bagdasarian},
     title = {On the interpolation properties  of certain quasilinearizable pairs},
     journal = {Sbornik. Mathematics},
     pages = {227--234},
     publisher = {mathdoc},
     volume = {189},
     number = {2},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_2_a1/}
}
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A. G. Bagdasarian. On the interpolation properties  of certain quasilinearizable pairs. Sbornik. Mathematics, Tome 189 (1998) no. 2, pp. 227-234. http://geodesic.mathdoc.fr/item/SM_1998_189_2_a1/