Complex interpolation with Dirichlet boundary conditions on the half line

Nick Lindemulder, Martin Meyries, Mark Veraar*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

13 Citations (Scopus)
44 Downloads (Pure)

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 languageEnglish
Pages (from-to)2435-2456
Number of pages22
JournalMathematische Nachrichten
Volume291
Issue number16
DOIs
Publication statusPublished - 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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