LAUSR

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.