The boundary Harnack principle and the 3 <i>G</i> principle in fractal‐type spaces

Abstract We prove a generalized version of the 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 , , 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 principle for these spaces. We also discuss applications to Schrödinger operators.