Potential Analysis

, Volume 5, Issue 2, pp 109-138

First online:

Perturbation of Dirichlet forms by measures

  • Peter StollmannAffiliated withFachbereich Mathematik, Universität Frankfurt
  • , Jürgen VoigtAffiliated withFachrichtung Mathematik, Technische Universität Dresden

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Perturbations of a Dirichlet form \(\mathfrak{h}\) by measures μ are studied. The perturbed form \(\mathfrak{h}\)−μ+ is defined for μ in a suitable Kato class and μ+ absolutely continuous with respect to capacity. L p-properties of the corresponding semigroups are derived by approximating μ by functions. For treating μ+, 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.

Mathematics Subject Classifications (1991)

Primary 47D07 Secondary 31C25

Key words

Dirichlet form measure perturbation substochastic semigroup capacity smooth measures