Perturbation of Dirichlet forms by measures (Q1917786)

This paper studies the perturbation of Dirichlet forms \({\mathfrak h}\) by measures \(\mu\). In this paper, the authors defined the perturbed form \({\mathfrak h}-\mu_-+ \mu_+\) for \(\mu_-\) in a suitable Kato class and \(\mu_+\) absolutely continuous with respect to the capacity. The main results of the paper are: (1) if the unperturbed semigroup has \(L_p\)-\(L_q\)-smoothing properties then the perturbed semigroup also has the properties; and (2) if the unperturbed semigroup is holomorphic in \(L_1\) then, for a larger class of measures \(\mu\), the perturbed semigroup also has the same property.