Interpolation Hilbert spaces between Sobolev spaces
Vladimir A. Mikhailets, Aleksandr A. Murach

TL;DR
This paper explicitly characterizes all Hilbert function spaces that serve as interpolation spaces between Sobolev spaces, showing they are a subclass of H"ormander spaces parametrized by specific radial functions.
Contribution
It provides a complete description of interpolation Hilbert spaces between Sobolev spaces, including explicit examples of intermediate but non-interpolation spaces.
Findings
Interpolation spaces form a subclass of H"ormander spaces
Parametrization by OR-varying radial functions at infinity
Explicit examples of non-interpolation intermediate spaces
Abstract
We explicitly describe all Hilbert function spaces that are interpolation spaces with respect to a given couple of Sobolev inner product spaces considered over or a half-space in 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 and satisfies some additional conditions. We give explicit examples of intermediate but not interpolation spaces.
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