On a normality criterion of Mandelbrojt

Extension of the classical Mandelbrojt's criterion for normality of a family of zero-free holomorphic functions of several complex variables is given. We show that a family of holomorphic functions of several complex variables whose corresponding Levi form is uniformly bounded away from zero is...

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Bibliographic Details
Published in:Complex variables and elliptic equations Vol. 59; no. 10; pp. 1388 - 1394
Main Author: Dovbush, P.V.
Format: Journal Article
Language:English
Published: Colchester Taylor & Francis 03.10.2014
Taylor & Francis Ltd
Subjects:
Complex variables
Criteria
holomorphic functions of several complex variables
Mathematical analysis
normal families
Normality
ISSN:1747-6933, 1747-6941
Online Access:Get full text
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Summary:Extension of the classical Mandelbrojt's criterion for normality of a family of zero-free holomorphic functions of several complex variables is given. We show that a family of holomorphic functions of several complex variables whose corresponding Levi form is uniformly bounded away from zero is normal.
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ISSN:1747-6933
1747-6941
DOI:10.1080/17476933.2013.854342