| Abstract: | In the paper, the interpolation properties of the spacesH
p
s
(v; ℝ
n
) of Sobolev-Liouville type and the spacesB
p, q
s
(μ 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(v
o
),H(v
1)} and {B(μ0),B(μ1)} 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.
Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 666–672, November, 1997.
Translated by A. I. Shtern |
