Lower and upper order of harmonic mappings

H. Arbeláez, R. Hernández, W. Sierra

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Article number125837
JournalJournal of Mathematical Analysis and Applications
Volume507
Issue number2
DOIs
StatePublished - 15 Mar 2022

Keywords

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

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