Results on meromorphic φ -normal functions

Rauno Aulaskari, Shamil Makhmutov, Jouni Rättyä

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Let φ: [0, 1) → (0, ∞) be an increasing function. A meromorphic function f in the unit disc is said to be φ -normal if its spherical derivative f#(z):=|f′(z)|/(1 +|f(z)|2) satisfies f#(z) = O{script} (φ(|z|)) as |z| → 1-. This article is devoted to the study of meromorphic φ-normal functions. In particular, an analogue of the Lohwater-Pommerenke theorem and several equivalent characterizations for φ-normal functions are established under certain regularity conditions on φ.

Original languageEnglish
Pages (from-to)855-863
Number of pages9
JournalComplex Variables and Elliptic Equations
Volume54
Issue number9
DOIs
Publication statusPublished - Sep 2009

Fingerprint

Normal Function
Meromorphic Function
Increasing Functions
Regularity Conditions
Unit Disk
Analogue
Derivative
Theorem
Derivatives

Keywords

  • Bloch function
  • Chordal distance
  • Meromorphic function
  • Normal family
  • Normal function
  • Spherical derivative
  • Unit disc

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

Results on meromorphic φ -normal functions. / Aulaskari, Rauno; Makhmutov, Shamil; Rättyä, Jouni.

In: Complex Variables and Elliptic Equations, Vol. 54, No. 9, 09.2009, p. 855-863.

Research output: Contribution to journalArticle

Aulaskari, Rauno ; Makhmutov, Shamil ; Rättyä, Jouni. / Results on meromorphic φ -normal functions. In: Complex Variables and Elliptic Equations. 2009 ; Vol. 54, No. 9. pp. 855-863.
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