Metric Properties of Capacities

  • David R. Adams
  • Lars Inge Hedberg
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 314)


Many problems have definitive solutions in terms of capacities, but the latter have the drawback that their geometrical meaning is not transparent. For this reason we devote most of this chapter to comparing the (α, p)-capacities C α, p for 1 < p < ∞ and 0 < αpN to the more geometric quantities known as Hausdorff measures. As we now know, C α, p is associated not only to the Sobolev spaces B α p, p and Bessel potential spaces L α, p , but also to the Besov spaces and the Lizorkin—Triebel spaces F α p, q , 1 < q < ∞.


Lipschitz Mapping Besov Space Comparison Theorem Hausdorff Measure Affine Subspace 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • David R. Adams
    • 1
  • Lars Inge Hedberg
    • 2
  1. 1.Department of MathematicsUniversity of KentuckyLexingtonUSA
  2. 2.Department of MathematicsLinköping UniversityLinköpingSweden

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