  We give an application of interpolation with a function parameter to
parabolic differential operators. We introduce the refined anisotropic Sobolev
scale that consists of some Hilbert function spaces of generalized smoothness.
The latter is characterized by a real number and a function varying slowly at
infinity in Karamata's sense. This scale is connected with anisotropic Sobolev
spaces by means of interpolation with a function parameter. We investigate a
general initial--boundary value parabolic problem in the refined Sobolev scale.
We prove that the operator corresponding to this problem sets isomorphisms
between appropriate spaces pertaining to this scale.
