Interpolation Hilbert Spaces Between Sobolev Spaces

We explicitly describe all Hilbert function spaces that are interpolation spaces with respect to a given couple of Sobolev inner product spaces considered over R-n or a half-space in R-n or a bounded Euclidean domain with Lipschitz boundary. We prove that these interpolation spaces form a subclass of isotropic Hormander spaces. They are parametrized with a radial function parameter which is OR-varying at +infinity and satisfies some additional conditions. We give explicit examples of intermediate but not interpolation spaces.