一类微分算子下调和映射的Bloch常数估计

IF 1.2 4区数学 Q1 MATHEMATICS

Acta Mathematica Scientia Pub Date : 2023-11-29 DOI:10.1007/s10473-024-0116-0

Jieling Chen, Mingsheng Liu

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引用次数: 0

摘要

本文首先得到了形式为\(L(f) = z{f_z} - \bar z{f_{\bar z}}\)的调和映射的一元半径和Bloch常数的精确值，其中f表示有界膨胀的归一化调和映射。然后，利用这些结果，我们给出了某些调和映射L(f)的Bloch常数的更好估计，其中f是k -准正则调和或开调和。最后，我们建立了三种形式为L(f)的双调和映射的Bloch-Landau型定理。这些结果在某些特定情况下是尖锐的，并且改进了早期作者的相关结果。

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Estimate on the Bloch constant for certain harmonic mappings under a differential operator

In this paper, we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the form \(L(f) = z{f_z} - \bar z{f_{\bar z}}\), where f represents normalized harmonic mappings with bounded dilation. Then, using these results, we present better estimations for the Bloch constants of certain harmonic mappings L(f), where f is a K-quasiregular harmonic or open harmonic. Finally, we establish three versions of Bloch-Landau type theorem for biharmonic mappings of the form L(f). These results are sharp in some given cases and improve the related results of earlier authors.

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来源期刊

Acta Mathematica Scientia 数学-数学

CiteScore

2.00

自引率

10.00%

发文量

2614

审稿时长

6 months

期刊介绍： Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981. The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.