Complex interpolation with Dirichlet boundary conditions on the half line

Nick Lindemulder; Martin Meyries; Mark Veraar

doi:10.1002/mana.201700204

Complex interpolation with Dirichlet boundary conditions on the half line

Nick Lindemulder, Martin Meyries, Mark Veraar^*

^*Corresponding author for this work

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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
Pages (from-to)	2435-2456
Number of pages	22
Journal	Mathematische Nachrichten
Volume	291
Issue number	16
DOIs	https://doi.org/10.1002/mana.201700204
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

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title = "Complex interpolation with Dirichlet boundary conditions on the half line",

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.",

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AU - Meyries, Martin

AU - Veraar, Mark

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KW - Complex interpolation with boundary conditions

KW - H∞-calculus

KW - Pointwise multipliers

KW - Sobolev spaces

KW - UMD

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ER -

Complex interpolation with Dirichlet boundary conditions on the half line

Abstract

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Keywords

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