Besov spaces on open sets

  title={Besov spaces on open sets},
  author={Tsukasa Iwabuchi and Tokio Matsuyama and Koichi Taniguchi},
This paper is devoted to giving definitions of Besov spaces on an arbitrary open set of $\mathbb R^n$ via the spectral theorem for the Schr\"odinger operator with the Dirichlet boundary condition. The crucial point is to introduce some test function spaces on $\Omega$. 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… CONTINUE READING