### 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 language | English |
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Pages (from-to) | 855-863 |

Number of pages | 9 |

Journal | Complex Variables and Elliptic Equations |

Volume | 54 |

Issue number | 9 |

DOIs | |

Publication status | Published - Sep 2009 |

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### 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

*Complex Variables and Elliptic Equations*,

*54*(9), 855-863. https://doi.org/10.1080/17476930902998860

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

Research output: Contribution to journal › Article

*Complex Variables and Elliptic Equations*, vol. 54, no. 9, pp. 855-863. https://doi.org/10.1080/17476930902998860

}

TY - JOUR

T1 - Results on meromorphic φ -normal functions

AU - Aulaskari, Rauno

AU - Makhmutov, Shamil

AU - Rättyä, Jouni

PY - 2009/9

Y1 - 2009/9

N2 - 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.

AB - 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.

KW - Bloch function

KW - Chordal distance

KW - Meromorphic function

KW - Normal family

KW - Normal function

KW - Spherical derivative

KW - Unit disc

UR - http://www.scopus.com/inward/record.url?scp=70449629402&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70449629402&partnerID=8YFLogxK

U2 - 10.1080/17476930902998860

DO - 10.1080/17476930902998860

M3 - Article

VL - 54

SP - 855

EP - 863

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

SN - 1747-6933

IS - 9

ER -