Abstract
Perturbations of a Dirichlet form \(\mathfrak{h}\) by measures μ are studied. The perturbed form \(\mathfrak{h}\)−μ−+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.
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Stollmann, P., Voigt, J. Perturbation of Dirichlet forms by measures. Potential Analysis 5, 109–138 (1996). https://doi.org/10.1007/BF00396775
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DOI: https://doi.org/10.1007/BF00396775