Differential Marty-type inequalities which lead to quasi-normality

Shahar Nevo; Ziv Shem Tov

doi:10.1016/j.jmaa.2023.127337

Differential Marty-type inequalities which lead to quasi-normality

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

Abstract

We show that a family of all holomorphic functions f in a domain D satisfying [Formula presented], for z∈D,m,k∈N,m≤k,C>0, is quasi-normal for α=1, and quasi-normal of order at most k−1 for α<1 (possibly negative) in D.

Original language	English
Article number	127337
Journal	Journal of Mathematical Analysis and Applications
Volume	527
Issue number	1P1
DOIs	https://doi.org/10.1016/j.jmaa.2023.127337
State	Published - 1 Nov 2023

Bibliographical note

Funding Information:
The authors thank the referee for his very valuable comments.

Publisher Copyright:
© 2023 Elsevier Inc.

Keywords

Differential inequalities
Marty's theorem
Quasi-normal families

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10.1016/j.jmaa.2023.127337

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KW - Quasi-normal families

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Differential Marty-type inequalities which lead to quasi-normality

Abstract

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Keywords

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