Differential inequalities and quasi-normal families

Roi Bar, Jürgen Grahl, Shahar Nevo

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We show that a family F of meromorphic functions in a domain D satisfying (Formula Presented.) (where k and j are integers with (Formula Presented.) are real numbers) is quasi-normal. Furthermore, if all functions in F are holomorphic, the order of quasi-normality of F is at most j-1. The proof relies on the Zalcman rescaling method and previous results on differential inequalities constituting normality.

Original languageEnglish
Pages (from-to)63-71
Number of pages9
JournalAnalysis and Mathematical Physics
Volume4
Issue number1-2
DOIs
StatePublished - 25 Jun 2014

Bibliographical note

Publisher Copyright:
© 2013, Springer Basel.

Keywords

  • Differential inequalities
  • Marty’s theorem
  • Normal families
  • Quasi-normal families
  • Zalcman’s lemma

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