Pre-Schwarzian and Schwarzian derivatives of logharmonic mappings

V. Bravo, R. Hernández, S. Ponnusamy, O. Venegas

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We introduce definitions of pre-Schwarzian and Schwarzian derivatives for logharmonic mappings, and basic properties such as the chain rule, multiplicative invariance and affine invariance are proved for these operators. It is shown that the pre-Schwarzian is stable only with respect to rotations of the identity. A characterization is given for the case when the pre-Schwarzian derivative is holomorphic.

Original languageEnglish
Pages (from-to)733-754
Number of pages22
JournalMonatshefte fur Mathematik
Volume199
Issue number4
DOIs
StatePublished - Dec 2022
Externally publishedYes

Keywords

  • Harmonic and logharmonic mappings
  • Pre-Schwarzian and Schwarzian derivatives
  • Univalence criterion

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