Distortion Theorems Associated with Schwarzian Derivative for Harmonic Mappings
Distortion Theorems Associated with Schwarzian Derivative for Harmonic Mappings
Authors
Hernández, Rodrigo
Venegas, Osvaldo
Venegas, Osvaldo
Authors
Date
2019-09-05
Datos de publicación:
Complex Analysis and Operator Theory, Vol. 13, N° 4, 1783-1793, 2019
Keywords
Teoremas de Distorsión - Mapeos Armónicos - Derivado de Schwarz
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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.