Complex interpolation with Dirichlet boundary conditions on the half line

Nick Lindemulder, Martin Meyries, Mark Veraar

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)
14 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

Keywords

  • Ap-weights
  • Bessel potential spaces
  • Complex interpolation with boundary conditions
  • H∞-calculus
  • Pointwise multipliers
  • Sobolev spaces
  • UMD

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