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- Title
Interpolation Hilbert Spaces Between Sobolev Spaces.
- Authors
Mikhailets, Vladimir; Murach, Aleksandr
- 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 $${\mathbb{R}^{n}}$$ 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 Hörmander 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.
- Publication
Results in Mathematics / Resultate der Mathematik, 2015, Vol 67, Issue 1/2, p135
- ISSN
1422-6383
- Publication type
Article
- DOI
10.1007/s00025-014-0399-x