Besov spaces on open sets

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5 Citations (Scopus)


This paper is devoted to giving definitions of Besov spaces on an arbitrary open set Ω of Rn via the spectral theorem for the Schrödinger operator with the Dirichlet boundary condition. The crucial point is to introduce some test function spaces on Ω. The fundamental properties of Besov spaces are also shown, such as embedding relations and duality, etc. Furthermore, the isomorphism relations are established among the Besov spaces in which regularity of functions is measured by the Dirichlet Laplacian and the Schrödinger operators.

Original languageEnglish
Pages (from-to)93-149
Number of pages57
JournalBulletin des Sciences Mathematiques
Publication statusPublished - 2019 May


  • Besov spaces
  • Potential of Kato class
  • Schrödinger operators

ASJC Scopus subject areas

  • Mathematics(all)


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