Interpolation Hilbert spaces between Sobolev 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 ${\mathbb{R}}^n$ 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 $+\infty$ and satisfies some additional conditions. We give explicit examples of intermediate but not interpolation spaces.

16 pages. Extended version. The final publication is available at Springer via http://dx.doi.org/10.1007/s00025-014-0399-x

References in corpus (1)

• Interpolation with a function parameter and refined scale of spaces

Cited by in corpus (9)

• Parameter-elliptic problems and interpolation with a function parameter
• Elliptic problems with boundary conditions of high orders in Hörmander spaces
• Elliptic boundary-value problems in Hörmander spaces
• Unconditional convergence of eigenfunction expansions for abstract and elliptic operators
• Nonregular elliptic boundary-value problems and Hörmander spaces
• Hörmander spaces on manifolds, and their application to elliptic boundary-value problems
• Elliptic operators on refined Sobolev scales on vector bundles
• An extended Hilbert scale and its applications
• Elliptic problems with nonclassical boundary conditions in an extended Sobolev scale