On radial behaviour and balanced Bloch functions.
Juan Jesús Donaire, Christian Pommerenke (1999)
Revista Matemática Iberoamericana
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A Bloch function g is a function analytic in the unit disk such that (1 - |z|2) |g' (z)| is bounded. First we generalize the theorem of Rohde that, for every bad Bloch function, g(rζ) (r → 1) follows any prescribed curve at a bounded distance for ζ in a set of Hausdorff dimension almost one. Then we introduce balanced Bloch functions. They are characterized by the fact that |g'(z)| does not vary much on each circle {|z| = r} except for small exceptional arcs. We show...