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arXiv · 1106.2049

Interpolation Hilbert spaces between Sobolev spaces

Vladimir A. Mikhailets·Aleksandr A. Murach
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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 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.

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Vladimir A. Mikhailets, Aleksandr A. Murach. 2011-06-10. Interpolation Hilbert spaces between Sobolev spaces. https://doi.org/10.1007/s00025-014-0399-x

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