Abstract
We prove results on complex interpolation of vector-valued Sobolev spaces over the half-line with Dirichlet boundary condition. Motivated by applications in evolution equations, the results are presented for Banach space-valued Sobolev spaces with a power weight. The proof is based on recent results on pointwise multipliers in Bessel potential spaces, for which we present a new and simpler proof as well. We apply the results to characterize the fractional domain spaces of the first derivative operator on the half line.
Original language | English |
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Pages (from-to) | 2435-2456 |
Number of pages | 22 |
Journal | Mathematische Nachrichten |
Volume | 291 |
Issue number | 16 |
DOIs | |
Publication status | Published - 2018 |
Bibliographical note
Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Keywords
- Ap-weights
- Bessel potential spaces
- Complex interpolation with boundary conditions
- H∞-calculus
- Pointwise multipliers
- Sobolev spaces
- UMD