Interpolation Hilbert spaces for a couple of Sobolev spaces

Details Interpolation Hilbert spaces for a couple of Sobolev spaces Interpolation Hilbert spaces for a couple of Sobolev spaces

2011-06-10

arxiv.org/abs/1106.2049v1

Mathematics

Functional Analysis

14 pages

Scientific paper

We describe all Hilbert spaces that are interpolation spaces with respect to a given couple of Sobolev inner product spaces over $\mathbb{R}^{n}$ or a bounded domain with a smooth 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 $RO$-varying at $+\infty$, considered as a function of $(1+|\xi|^{2})^{1/2}$ with $\xi\in\mathbb{R}^{n}$.

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