Equivalent semi-norms of non-local Dirichlet forms on the Sierpiński gasket and applications (Q1662911)

The author constructs equivalent semi-norms of non-local Dirichlet forms on the Sierpiński gasket \(K\) and obtains a monotone convergence result for all functions in \(L^2 (K, \nu)\), where \(\nu\) denotes the normalized Hausdorff measure on \(K\). This convergence result implies also a Mosco convergence. In addition, an explicit construction of a sequence of non-local Dirichlet forms with jumping kernels equivalent to \(|x-y|^{-\alpha-\beta}\) converging to a local Dirichlet form is presented.