On the interpolation properties of certain quasilinearizable pairs

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).