@article{807a47604afc40c9bb023adb8015c9c3,
title = "Lower and upper order of harmonic mappings",
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.",
keywords = "Concave functions, Harmonic mapping, Linearly connected domain, Lower order, Schwarzian derivative, Upper order",
author = "H. Arbel{\'a}ez and R. Hern{\'a}ndez and W. Sierra",
note = "Funding Information: The first author was partially supported by the Universidad Nacional de Colombia , Hermes code 49148 . The second author is supported by grant FONDECYT # 1190756 , Chile. The third author thanks the Universidad del Cauca for providing time for this work through research project VRI ID 5464 . Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",
year = "2022",
month = mar,
day = "15",
doi = "10.1016/j.jmaa.2021.125837",
language = "English",
volume = "507",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
number = "2",
}