Mathematische Zeitschrift

, Volume 257, Issue 3, pp 525–545

Doubling measures, monotonicity, and quasiconformality

Article

Abstract

We construct quasiconformal mappings in Euclidean spaces by integration of a discontinuous kernel against doubling measures with suitable decay. The differentials of mappings that arise in this way satisfy an isotropic form of the doubling condition. We prove that this isotropic doubling condition is satisfied by the distance functions of certain fractal sets. Finally, we construct an isotropic doubling measure that is not absolutely continuous with respect to the Lebesgue measure.

Mathematics Subject Classification (2000)

30C65 28A75 42A55 47H05 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Leonid V. Kovalev
    • 1
  • Diego Maldonado
    • 2
    • 3
  • Jang-Mei Wu
    • 4
  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA
  3. 3.Department of MathematicsKansas State UniversityManhattanUSA
  4. 4.Department of MathematicsUniversity of IllinoisUrbanaUSA

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