Mathematical Notes

, Volume 104, Issue 5–6, pp 683–688 | Cite as

Lemniscate Zone and Distortion Theorems for Multivalent Functions. II

  • V. N. DubininEmail author


For meromorphic circumferentially mean p-valent functions, an analog of the classical distortion theorem is proved. It is shown that the existence of connected lemniscates of the function and a constraint on a cover of two given points lead to an inequality involving the Green energy of a discrete signedmeasure concentrated at the zeros of the given function and the absolute values of its derivatives at these zeros. This inequality is an equality for the superposition of a certain univalent function and an appropriate Zolotarev fraction.


meromorphic function p-valent function lemniscate Zolotarev fraction symmetrization 


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Far-Eastern Federal UniversityVladivostokRussia
  2. 2.Institute for Applied Mathematics, Far-Eastern BranchRussian Academy of SciencesVladivostokRussia

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