On a Normality Criterion of W. Schwick

In this paper, as an application of Zalcman’s lemma in C n , we give a sufficient condition for normality of a family of holomorphic functions of several complex variables, which generalizes previous known one-dimensional results of H.L. Royden and W. Schwick.

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Bibliographic Details
Published in:The Journal of geometric analysis Vol. 31; no. 5; pp. 5355 - 5358
Main Author: Dovbush, P. V.
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2021
Springer Nature B.V
Subjects:
Abstract Harmonic Analysis
Analytic functions
Complex variables
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Mathematical analysis
Mathematics
Mathematics and Statistics
Normal families
32A19
Holomorphic functions of several complex variables
Zalcman’s Lemma
ISSN:1050-6926, 1559-002X
Online Access:Get full text
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Summary:In this paper, as an application of Zalcman’s lemma in C n , we give a sufficient condition for normality of a family of holomorphic functions of several complex variables, which generalizes previous known one-dimensional results of H.L. Royden and W. Schwick.
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ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-020-00481-4