Spherical derivatives and normal families

Jürgen Grahl; Shahar Nevo

doi:10.1007/s11854-012-0016-4

Spherical derivatives and normal families

Jürgen Grahl, Shahar Nevo

Department of Mathematics

University of Würzburg

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

20 Scopus citations

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

Bibliographical 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.

Funding

∗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.

Funders	Funder number
German Israeli Foundation for Scientific Research and Development
European Science Foundation
Israel Science Foundation	395/07

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10.1007/s11854-012-0016-4

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Spherical derivatives and normal families

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Bibliographical note

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