CONVERGENCE OF DIRICHLET FORMS AND BESOV NORMS ON SCALE IRREGULAR SIERPIŃSKI GASKETS

Jin Gao (), Zhenyu Yu and Junda Zhang ()
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Jin Gao: Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, P. R. China
Zhenyu Yu: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China
Junda Zhang: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 07, 1-14

Abstract: In this paper, we construct equivalent semi-norms of local and non-local Dirichlet forms on scale irregular Sierpiński gaskets. These fractals are not necessarily self-similar, and have volume doubling Hausdorff measures which are not necessarily Ahlfors regular. We obtain that a sequence of non-local Dirichlet forms converges to a local Dirichlet form, which extends a convergence theorem of Bourgain, Brezis and Mironescu to the scale irregular Sierpiński gaskets for p = 2.

Keywords: Convergence; Dirichlet Form; Random Fractals; Doubling Measure (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22501638

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