Spherical derivatives and normal families

Jürgen Grahl; Shahar Nevo

doi:https://doi.org/10.1007/s11854-012-0016-4

Spherical derivatives and normal families

Jürgen Grahl, Shahar Nevo

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

We show that a family of functions meromorphic in a plane domain D whose spherical derivatives are uniformly bounded away from zero is normal. Furthermore, we show that for each f meromorphic in the unit disk D, inf_z∈Df^#(z) ≤ 1/2, where f^# denotes the spherical derivative of f.

Original language	English
Pages (from-to)	119-128
Number of pages	10
Journal	Journal d'Analyse Mathematique
Volume	117
Issue number	1
DOIs	https://doi.org/10.1007/s11854-012-0016-4
State	Published - Jun 2012

All Science Journal Classification (ASJC) codes

Analysis
General Mathematics

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https://doi.org/10.1007/s11854-012-0016-4

Cite this

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title = "Spherical derivatives and normal families",

abstract = "We show that a family of functions meromorphic in a plane domain D whose spherical derivatives are uniformly bounded away from zero is normal. Furthermore, we show that for each f meromorphic in the unit disk D, infz∈Df#(z) ≤ 1/2, where f# denotes the spherical derivative of f.",

author = "J{\"u}rgen Grahl and Shahar Nevo",

note = "Funding Information: ∗Part of this work was supported by the German Israeli Foundation for Scientific Research and Development (No. G 809−234.6/2003). Shahar Nevo also received support from the Israel Science Foundation, Grant No. 395/07. This research is part of the European Science Foundation Networking Programme HCAA.",

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AB - We show that a family of functions meromorphic in a plane domain D whose spherical derivatives are uniformly bounded away from zero is normal. Furthermore, we show that for each f meromorphic in the unit disk D, infz∈Df#(z) ≤ 1/2, where f# denotes the spherical derivative of f.

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Spherical derivatives and normal families

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All Science Journal Classification (ASJC) codes

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