Potential Analysis

, Volume 5, Issue 2, pp 109–138

Perturbation of Dirichlet forms by measures

  • Peter Stollmann
  • Jürgen Voigt

DOI: 10.1007/BF00396775

Cite this article as:
Stollmann, P. & Voigt, J. Potential Analysis (1996) 5: 109. doi:10.1007/BF00396775


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. Lp-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 Lp-Lq-smoothing properties the same is shown to hold for the perturbed semigroup. If the unperturbed semigroup is holomorphic on L1 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 

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Peter Stollmann
    • 1
  • Jürgen Voigt
    • 2
  1. 1.Fachbereich MathematikUniversität FrankfurtFrankfurtGermany
  2. 2.Fachrichtung MathematikTechnische Universität DresdenDresdenGermany

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