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The boundary Harnack principle and the 3G principle in fractal‐type spaces

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  • Anthony Graves‐McCleary
  • Laurent Saloff‐Coste

Abstract

We prove a generalized version of the 3G$3G$ Principle for Green's functions on bounded inner uniform domains in a wide class of Dirichlet spaces. In particular, our results apply to higher‐dimensional fractals such as Sierpinski carpets in Rn$\mathbf {R}^n$, n≥3$n\ge 3$, as well as generalized fractal‐type spaces that do not have a well‐defined Hausdorff dimension or walk dimension. This yields new instances of the 3G$3G$ principle for these spaces. We also discuss applications to Schrödinger operators.

Suggested Citation

  • Anthony Graves‐McCleary & Laurent Saloff‐Coste, 2025. "The boundary Harnack principle and the 3G principle in fractal‐type spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 298(11), pages 3554-3575, November.
    • Handle: RePEc:bla:mathna:v:298:y:2025:i:11:p:3554-3575
    DOI: 10.1002/mana.70059
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