Differential inequalities and quasi-normal families

Roi Bar; Jürgen Grahl; Shahar Nevo

doi:10.1007/s13324-013-0064-7

Differential inequalities and quasi-normal families

Roi Bar
, Jürgen Grahl
, Shahar Nevo

Department of Mathematics

Bar-Ilan University
University of Würzburg

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

6 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 language	English
Pages (from-to)	63-71
Number of pages	9
Journal	Analysis and Mathematical Physics
Volume	4
Issue number	1-2
DOIs	https://doi.org/10.1007/s13324-013-0064-7
State	Published - 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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10.1007/s13324-013-0064-7

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AU - Grahl, Jürgen

AU - Nevo, Shahar

PY - 2014/6/25

Y1 - 2014/6/25

N2 - 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.

AB - 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.

KW - Differential inequalities

KW - Marty’s theorem

KW - Normal families

KW - Quasi-normal families

KW - Zalcman’s lemma

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IS - 1-2

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Differential inequalities and quasi-normal families

Abstract

Bibliographical note

Keywords

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