Spaces of generalized smoothness on $h$-sets and related Dirichlet forms

Volume 174 / 2006

V. Knopova, M. Zähle Studia Mathematica 174 (2006), 277-308 MSC: 46E35, 42B35, 28A80, 60J75. DOI: 10.4064/sm174-3-4

Abstract

The paper is devoted to spaces of generalized smoothness on so-called $h$-sets. First we find quarkonial representations of isotropic spaces of generalized smoothness on $\mathbb{R}^n$ and on an $h$-set. Then we investigate representations of such spaces via differences, which are very helpful when we want to find an explicit representation of the domain of a Dirichlet form on $h$-sets. We prove that both representations are equivalent, and also find the domain of some time-changed Dirichlet form on an $h$-set.

Authors

  • V. KnopovaMathematical Institute
    University of Jena
    Ernst-Abbe-Platz 2
    07743 Jena, Germany
    e-mail
  • M. ZähleMathematical Institute
    University of Jena
    Ernst-Abbe-Platz 2
    07743 Jena, Germany
    e-mail

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