On the domains of Dirichlet forms on metric measure spaces

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Abstract

We prove that the domain of the local Dirichlet form is strictly contained in the domain of any stable-like non-local Dirichlet form on general metric measure spaces. We construct explicit functions in the difference of the domains of the Dirichlet forms on the Sierpiński gasket and the Sierpiński carpet.

Original languageEnglish
Pages (from-to)2129-2154
Number of pages26
JournalMathematische Zeitschrift
Volume301
Issue number2
DOIs
Publication statusPublished - Feb 2022

Keywords

  • Dirichlet form
  • Sierpiński carpet
  • Sierpiński gasket
  • Sobolev space

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