Lower and upper order of harmonic mappings

H. Arbeláez; R. Hernández; W. Sierra

doi:10.1016/j.jmaa.2021.125837

Lower and upper order of harmonic mappings

H. Arbeláez, R. Hernández, W. Sierra

Faculty of Engineering and Science

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper, we define both the upper and lower order of a sense-preserving harmonic mapping in D. We generalize to the harmonic case some known results about holomorphic functions with positive lower order and we show some consequences of a function having finite upper order. In addition, we improve a related result in the case when there is equality in a known distortion theorem for harmonic mappings with finite upper order. Some examples are provided to illustrate the developed theory.

Original language	English
Article number	125837
Journal	Journal of Mathematical Analysis and Applications
Volume	507
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2021.125837
State	Published - 15 Mar 2022

Keywords

Concave functions
Harmonic mapping
Linearly connected domain
Lower order
Schwarzian derivative
Upper order

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10.1016/j.jmaa.2021.125837

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AU - Hernández, R.

AU - Sierra, W.

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AB - In this paper, we define both the upper and lower order of a sense-preserving harmonic mapping in D. We generalize to the harmonic case some known results about holomorphic functions with positive lower order and we show some consequences of a function having finite upper order. In addition, we improve a related result in the case when there is equality in a known distortion theorem for harmonic mappings with finite upper order. Some examples are provided to illustrate the developed theory.

KW - Concave functions

KW - Harmonic mapping

KW - Linearly connected domain

KW - Lower order

KW - Schwarzian derivative

KW - Upper order

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Lower and upper order of harmonic mappings

Abstract

Keywords

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