Perturbation of Dirichlet forms by measures

Perturbations of a Dirichlet form h by measures mu are studied. The perturbed form h-mu(-)+ mu(+) is defined for mu(-) in a suitable Kato class and mu(+) absolutely continuous with respect to capacity. L(p)-properties of the corresponding semigroups are derived by approximating mu(-) by functions. For treating mu(+), a criterion for domination of positive semigroups is proved. If the unperturbed semigroup has L(p)-L(q)-smoothing properties the same is shown to hold for the perturbed semigroup. If the unperturbed semigroup is holomorphic on L(1) the same is shown to be true for the perturbed semigroup, for a large class of measures.