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Complex interpolation with Dirichlet boundary conditions on the half line

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  • Nick Lindemulder
  • Martin Meyries
  • Mark Veraar

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.

Suggested Citation

  • Nick Lindemulder & Martin Meyries & Mark Veraar, 2018. "Complex interpolation with Dirichlet boundary conditions on the half line," Mathematische Nachrichten, Wiley Blackwell, vol. 291(16), pages 2435-2456, November.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:16:p:2435-2456
    DOI: 10.1002/mana.201700204
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    Cited by:

    1. Antonio Agresti & Nick Lindemulder & Mark Veraar, 2023. "On the trace embedding and its applications to evolution equations," Mathematische Nachrichten, Wiley Blackwell, vol. 296(4), pages 1319-1350, April.

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