artículo
SCHWARZIAN DERIVATIVES OF CONVEX MAPPINGS
Fecha
2011Registro en:
10.5186/aasfm.2011.3628
1798-2383
1239-629X
WOS:000295069400005
Autor
Chuaqui, Martin
Duren, Peter
Osgood, Brad
Institución
Resumen
A simple proof is given for Nehari's theorem that an analytic function f which maps the unit disk onto a convex region has Schwarzian norm parallel to f parallel to <= 2. The inequality in sharper form leads to the conclusion that no convex mapping with parallel to f parallel to = 2 can map onto a quasidisk. In particular, every bounded convex mapping has Schwarzian norm parallel to f parallel to < 2. The analysis involves a structural formula for the pre-Schwarzian of a convex mapping, which is studied in further detail.