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Convergence Of Dirichlet Forms And Besov Norms On Scale Irregular Sierpiåƒski Gaskets

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jin Gao & Zhenyu Yu & Junda Zhang, 2022. "Convergence Of Dirichlet Forms And Besov Norms On Scale Irregular Sierpiåƒski Gaskets," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(07), pages 1-14, November.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:07:n:s0218348x22501638
    DOI: 10.1142/S0218348X22501638
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