Bohr Type Inequalities for Functions with a Multiple Zero at the Origin

Recently, there has been a number of good deal of research on the Bohr’s phenomenon in various settings including a refined formulation of his classical version of the inequality. Among them, in Paulsen et al. (Proc Lond Math Soc 85(2):493–512, 2002) the authors considered cases in which the above f...

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Veröffentlicht in:Computational methods and function theory Jg. 20; H. 3-4; S. 559 - 570
Hauptverfasser: Ponnusamy, S., Wirths, K.-J.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2020
Springer Nature B.V
Schlagworte:
Analysis
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Schwarz lemma
Bohr’s inequality
Cauchy–Schwarz inequality
30B10
Primary 30A10
30C55
41A58
Analytic functions
Secondary 30C45
Multiple zero
ISSN:1617-9447, 2195-3724
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Zusammenfassung:Recently, there has been a number of good deal of research on the Bohr’s phenomenon in various settings including a refined formulation of his classical version of the inequality. Among them, in Paulsen et al. (Proc Lond Math Soc 85(2):493–512, 2002) the authors considered cases in which the above functions have a multiple zero at the origin. In this article, we present a refined version of Bohr’s inequality for these cases and give a partial answer to a question from Paulsen et al. (2002) for the revised setting.
Bibliographie:ObjectType-Article-1
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ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-020-00330-z