Quasi-normality induced by differential inequalities

Jürgen Grahl; Shahar Nevo

doi:10.1112/blms.12111

Quasi-normality induced by differential inequalities

Jürgen Grahl
, Shahar Nevo

Department of Mathematics

Bar-Ilan University

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

Abstract

We show that the family F_k of all meromorphic functions f in a domain D satisfying (Formula presented.) (where k is a natural number and C > 0) is quasi-normal. The proof relies mainly on the Zalcman–Pang rescaling lemma which we employ to get estimates for the behaviour of certain quotients of higher derivatives of the functions in F_k at certain points close to a point of non-normality.

Original language	English GB
Pages (from-to)	73-84
Number of pages	12
Journal	Bulletin of the London Mathematical Society
Volume	50
Issue number	1
DOIs	https://doi.org/10.1112/blms.12111
State	Published - 1 Feb 2018

Keywords

30A10 (primary)
30D45

ASJC Scopus subject areas

General Mathematics

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10.1112/blms.12111

Cite this

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title = "Quasi-normality induced by differential inequalities",

abstract = "We show that the family Fk of all meromorphic functions f in a domain D satisfying (Formula presented.) (where k is a natural number and C > 0) is quasi-normal. The proof relies mainly on the Zalcman–Pang rescaling lemma which we employ to get estimates for the behaviour of certain quotients of higher derivatives of the functions in Fk at certain points close to a point of non-normality.",

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AU - Nevo, Shahar

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AB - We show that the family Fk of all meromorphic functions f in a domain D satisfying (Formula presented.) (where k is a natural number and C > 0) is quasi-normal. The proof relies mainly on the Zalcman–Pang rescaling lemma which we employ to get estimates for the behaviour of certain quotients of higher derivatives of the functions in Fk at certain points close to a point of non-normality.

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KW - 30D45

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U2 - 10.1112/blms.12111

DO - 10.1112/blms.12111

M3 - مقالة

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EP - 84

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

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ER -

Quasi-normality induced by differential inequalities

Abstract

Keywords

ASJC Scopus subject areas

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