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Journal d'Analyse Mathématique

, Volume 133, Issue 1, pp 335–359 | Cite as

Extremal functions for modules of systems of measures

  • Melkana Brakalova
  • Irina Markina
  • Alexander Vasil’ev
Article

Abstract

We extend a result by Rodin, which provides an explicit method for finding the extremal function and the 2-module of a foliated family of curves in R2, to R n making use of Fuglede’s p-module of systems of measures. The extremal functions are identified and the p-module of systems of measures is computed in condensers of rather general type and in their images under homeomorphisms of certain regularity. At the beginning, we discuss and apply Rodin’s Theorem in order to obtain estimates for the conformal modules of parallelograms and ring domains in terms of directional dilatations.

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Copyright information

© Hebrew University Magnes Press 2017

Authors and Affiliations

  • Melkana Brakalova
    • 1
  • Irina Markina
    • 2
  • Alexander Vasil’ev
  1. 1.Department of MathematicsFordham UniversityBronxUSA
  2. 2.Department of MathematicsUniversity of BergenBergenNorway

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