On the domains of Dirichlet forms on metric measure spaces

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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
Issue number2
Publication statusPublished - Feb 2022


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


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