Mathematische Annalen

, Volume 334, Issue 3, pp 643–678 | Cite as

Global comparison of perturbed Green functions

  • Wolfhard HansenEmail author


Given a Green function G (e.g. with respect to (−Δ) α /2, 0<α≤2) on a region X where G has a generalized triangle property and given a (G-bounded) signed measure μ on X, necessary and sufficient conditions are given for the existence of a perturbed Green function which is comparable with G. This is done in the general setting of measurable spaces. Applications to C 1,1-regions in R d and, for the classical case α=2, to finitely connected regions in ℝ2 are given.


General Setting Green Function Measurable Space Classical Case Global Comparison 
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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany

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