Capacitary upper estimates for symmetric Dirichlet forms (Q1398028)

Let \(({\mathcal E},{\mathcal F})\) be a symmetric regular Dirichlet form on \(L^2(X,m)\), where \(X\) is a locally compact separable metric space and \(m\) is a Radon measure on \(X\) with full support. In this setting the author provides a general method for obtaining upper estimates for capacities in terms of upper estimates for energy of cut-off functions in both local and non-local case. The author further studies capacitary inequalities for the skew product of two symmetric Dirichlet forms. The last part of the paper is devoted to upper estimates for capacities for subordinate processes, in particular in the case when the underlying process is a special singular diffusion.