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Journal of Mathematical Sciences

, Volume 234, Issue 5, pp 608–615 | Cite as

Modules of Families of Vector Measures on a Riemann Surface

  • Yu. V. Dymchenko
  • V. A. Shlyk
Article

The paper considers a Riemann surface (in a broad sense of the term in the Hurwitz–Courant terminology) and an open set with a compact closure on this surface. It is proved that, following Aikawa–Ohtsuka, with a condenser on a given open set one can associate a family of vector measures, whose modules are computed directly with the aid of the weighted capacity (with Muchenhoupt weight) of the condenser.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Far Eastern Federal UniversityVladivostokRussia
  2. 2.Vladivostok Branch of the Russian Customs AcademyVladivostokRussia

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