Título inglés | On radial behaviour and balanced Bloch functions. |
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Título español | Comportamiento radial y funciones de Bloch equilibradas. |
Autor/es | Donaire, Juan Jesús ; Pommerenke, Christian |
Organización | Dep. Mat. Univ. Autòn. Barcelona, Barcelona, España;Dep. Mat. Tech. Univ. Berlin, Berlín, Alemania |
Revista | 0213-2230 |
Publicación | 1999, 15 (3): 429-449, 27 Ref. |
Tipo de documento | articulo |
Idioma | Inglés |
Resumen inglés | 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 e.g. that ∫01 |g'(rζ)|dr < ∞ holds either for all ζ Î T or for none. |
Clasificación UNESCO | 120223 |
Palabras clave español | Funciones analíticas ; Aplicación conforme |
Código MathReviews | MR1742212 |
Código Z-Math | Zbl 0948.30039 |
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