Problemy Analiza (2019-06-01)

Harmonic mappings onto R-convex domains

  • Graf S. Yu.

DOI
https://doi.org/10.15393/j3.art.2019.6190
Journal volume & issue
Vol. 8(26), no. 2
pp. 37 – 50

Abstract

Read online

The plane domain D is called R-convex if D contains each compact set bounded by two shortest sub-arcs of the radius R with endpoints w1, w2 ∈ D, |w1−w2| <= 2R. In this paper, we prove the conditions of R-convexity for images of disks under harmonic sense preserving functions. The coefficient bounds for harmonic mappings of the unit disk onto R-convex domains are obtained.

Keywords