EXTREME POINTS AND SUPPORT POINTS OF HARMONIC alpha-BLOCH MAPPINGS

摘要

We consider the problem of existence of the extreme points and support points of harmonic alpha-Bloch mappings and little harmonic alpha-Bloch mappings. First, we prove a necessary condition for a little harmonic alpha-Bloch mapping to be an extreme point of the unit ball of the normalized little harmonic alpha-Bloch spaces in the unit disk D, and we also show that a harmonic alpha-Bloch unit-valued set consists of several simple closed pairwise disjoint analytic curves and several isolated points. Then we show that a harmonic alpha-Bloch mapping f is a support point of the unit ball of the normalized harmonic alpha-Bloch spaces in D if and only if the alpha-Bloch unit-valued set of f is not empty. We also give a characterization for the support points of the unit ball of the harmonic alpha-Bloch spaces in D.