On radial behaviour and balanced Bloch functions

• Autores: Juan Jesús Donaire Benito, Christian Pommerenke
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 15, Nº 3, 1999, págs. 429-449
• Idioma: inglés
• Títulos paralelos:
  • Comportamiento radial y funciones de Bloch equilibradas.
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• Resumen

  • A Bloch function g is a function analytic in the unit disk such that (1 - / z / elevado a 2) g' (z) / is bounded. First we generalize the theorem of Rohde that, for every "bad" Bloch function, g(r dseta) (r --- 1) follows any prescribed curve at a bounded distance for dseta 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 e.g. that.