Distortion Theorems Associated with Schwarzian Derivative for Harmonic Mappings

Rodrigo Hernández; Osvaldo Venegas

doi:10.1007/s11785-018-0836-z

Distortion Theorems Associated with Schwarzian Derivative for Harmonic Mappings

Rodrigo Hernández
, Osvaldo Venegas

Faculty of Engineering and Science

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

2 Scopus citations

Abstract

Let f be a complex-valued harmonic mapping defined in the unit disc D. The theorems of Chuaqui and Osgood (J Lond Math Soc 2:289–298, 1993), which assert that the bounds of the size of the hyperbolic norm of the Schwarzian derivative for an analytic function f imply certain bounds for distortion and growth of f, are extended to the harmonic case.

Original language	English
Pages (from-to)	1783-1793
Number of pages	11
Journal	Complex Analysis and Operator Theory
Volume	13
Issue number	4
DOIs	https://doi.org/10.1007/s11785-018-0836-z
State	Published - 1 Jun 2019

Keywords

Distortion theorems
Harmonic mappings
Schwarzian derivative

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10.1007/s11785-018-0836-z

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abstract = "Let f be a complex-valued harmonic mapping defined in the unit disc D. The theorems of Chuaqui and Osgood (J Lond Math Soc 2:289–298, 1993), which assert that the bounds of the size of the hyperbolic norm of the Schwarzian derivative for an analytic function f imply certain bounds for distortion and growth of f, are extended to the harmonic case.",

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N2 - Let f be a complex-valued harmonic mapping defined in the unit disc D. The theorems of Chuaqui and Osgood (J Lond Math Soc 2:289–298, 1993), which assert that the bounds of the size of the hyperbolic norm of the Schwarzian derivative for an analytic function f imply certain bounds for distortion and growth of f, are extended to the harmonic case.

AB - Let f be a complex-valued harmonic mapping defined in the unit disc D. The theorems of Chuaqui and Osgood (J Lond Math Soc 2:289–298, 1993), which assert that the bounds of the size of the hyperbolic norm of the Schwarzian derivative for an analytic function f imply certain bounds for distortion and growth of f, are extended to the harmonic case.

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KW - Harmonic mappings

KW - Schwarzian derivative

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Distortion Theorems Associated with Schwarzian Derivative for Harmonic Mappings

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Keywords

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