• Uniformly locally univalent harmonic mappings

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/128/03/0032

• # Keywords

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

• # Abstract

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 $\mathcal{B}_{H}(\lambda)$.

• # Author Affiliations

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

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019