%0 Journal Article
%T Interpolation Hilbert spaces between Sobolev spaces
%A Vladimir A. Mikhailets
%A Aleksandr A. Murach
%J Mathematics
%D 2011
%I arXiv
%R 10.1007/s00025-014-0399-x
%X We explicitly describe all Hilbert function spaces that are interpolation spaces with respect to a given couple of Sobolev inner product spaces considered over $\mathbb{R}^{n}$ or a half-space in $\mathbb{R}^{n}$ or a bounded Euclidean domain with Lipschitz boundary. We prove that these interpolation spaces form a subclass of isotropic H\"ormander spaces. They are parametrized with a radial function parameter which is OR-varying at $+\infty$ and satisfies some additional conditions. We give explicit examples of intermediate but not interpolation spaces.
%U http://arxiv.org/abs/1106.2049v3