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.
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This research was supported by grant no. 03-01-12 of National Academy of Sciences of Ukraine (under the joint Ukrainian–Russian project of NAS of Ukraine and the Siberian Branch of Russian Academy of Sciences).
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Mikhailets, V.A., Murach, A.A. Interpolation Hilbert Spaces Between Sobolev Spaces. Results. Math. 67, 135–152 (2015). https://doi.org/10.1007/s00025-014-0399-x
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DOI: https://doi.org/10.1007/s00025-014-0399-x