Uniformly locally univalent harmonic mappings

Proceedings of the Indian Academy of Sciences. Mathematical sciences

JINJING QIAO^2¹  SAMINATHAN PONNUSAMY^1²  XIANTAO WANG^3³ 

[1] Department of Mathematics, Hebei University, Baoding 071002, Hebei, People’s Republic of China^2;Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India^1;Department of Mathematics, Shantou University, Shantou 515063, Guangdong, People’s Republic of China^3

关键词: Harmonic mapping;    pre-Schwarzian derivatives;    uniformly locally univalence;    growth estimate;    coefficient estimate;    harmonic Bloch space;    Hardy space;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

The primary aim of this paper is to characterize the uniformly locally univalent harmonic mappings in the unit disk. Then, we obtain sharp distortion, growth and covering theorems for one parameter family $\mathcal{B}_{H}(\lambda)$ of uniformly locally univalent harmonic mappings. Finally, we show that the subclass of $k$-quasiconformal harmonic mappings in $\mathcal{B}_{H}(\lambda)$ and the class $\mathcal{B}_{H}(\lambda)$ are contained in the Hardy space of a specific exponent depending on $\lambda$, respectively, and we also discuss the growth of coefficients for harmonic mappings in $\mathcal{B}_{H}(\lambda)$.

【 授权许可】

CC BY