Sharp bounds for the growth and distortion of the analytic part of convex harmonic functions
Abstract
We obtain the sharp upper and lower bounds for the growth and distortion of the analytic parts h of orientation-preserving harmonic mappings f = h + g ‾ (normalized in the standard way) that map the unit disk onto a convex domain. We show that the bounds are attained only by the so-called half-plane harmonic mapping or one of its rotations.
Fields of Study & Subjects
Analytic and geometric function theory
Holomorphic and Operator Theory
Meromorphic and Entire Functions
Publication details
- Journal / source
- Journal of Mathematical Analysis and Applications
- Volume
- 565
- Issue
- 1
- Pages
- 130949–130949
- Publication date
- 10 July 2026
- Language
- EN