On the interpolation of some generalized function spaces of different anisotropy

In the paper, the interpolation properties of the spaces $H_p^s(\nu;\mathbb R_n)$ of Sobolev–Liouville type and the spaces $B_{p,q}^s(\mu;\mathbb R_n)$ of Nikol'skii–Besov type generated by functions of polynomial growth that are infinitely differentiable outside of the origin are studied. Interpolation formulas for the pairs $\{H(\nu_0),H(\nu_1)\}$ and $\{B(\mu_0),B(\mu_1)\}$ of spaces of the above types for which the anisotropies of the interpolated spaces do not depend on each other are proved. The investigated spaces, for certain specification of the generating functions, coincide with the classical (isotropic and anisotropic) Sobolev–Liouville and Nikol'skii–Besov spaces.