On the Pre-Schwarzian Norm of Certain Logharmonic Mappings

IF 1 3区数学 Q1 MATHEMATICS

Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-02-27 DOI:10.1007/s40840-024-01668-6

Md Firoz Ali, Sushil Pandit

引用次数: 0

Abstract

We connect the pre-Schwarzian norm of logharmonic mappings to the pre-Schwarzian norm of an analytic function and establish some necessary and sufficient conditions under which locally univalent logharmonic mappings have a finite pre-Schwarzian norm. We also obtain a necessary and sufficient condition for a logharmonic function to be Bloch. Furthermore, we obtain the pre-Schwarzian norm and growth theorem for logharmonic Bloch mappings and their analytic and co-analytic parts.

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论某些对数谐波映射的前施瓦茨规范

我们将对数调和映射的前施瓦兹规范与解析函数的前施瓦兹规范联系起来，并建立了一些必要和充分条件，在这些条件下，局部单等的对数调和映射具有有限的前施瓦兹规范。我们还得到了对数谐函数是布洛赫函数的必要和充分条件。此外，我们还得到了对数谐波布洛赫映射及其解析部分和共解析部分的前施瓦茨规范和增长定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Bulletin of the Malaysian Mathematical Sciences Society 数学-数学

CiteScore

2.40

自引率

8.30%

发文量

176

审稿时长

3 months

期刊介绍： This journal publishes original research articles and expository survey articles in all branches of mathematics. Recent issues have included articles on such topics as Spectral synthesis for the operator space projective tensor product of C*-algebras; Topological structures on LA-semigroups; Implicit iteration methods for variational inequalities in Banach spaces; and The Quarter-Sweep Geometric Mean method for solving second kind linear fredholm integral equations.