# On radial behaviour and balanced Bloch functions.

Juan Jesús Donaire; Christian Pommerenke

Revista Matemática Iberoamericana (1999)

- Volume: 15, Issue: 3, page 429-449
- ISSN: 0213-2230

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topDonaire, Juan Jesús, and Pommerenke, Christian. "On radial behaviour and balanced Bloch functions.." Revista Matemática Iberoamericana 15.3 (1999): 429-449. <http://eudml.org/doc/39582>.

@article{Donaire1999,

abstract = {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 ∈ T or for none.},

author = {Donaire, Juan Jesús, Pommerenke, Christian},

journal = {Revista Matemática Iberoamericana},

keywords = {Funciones analíticas; Aplicación conforme; Bloch functions; conformal mappings},

language = {eng},

number = {3},

pages = {429-449},

title = {On radial behaviour and balanced Bloch functions.},

url = {http://eudml.org/doc/39582},

volume = {15},

year = {1999},

}

TY - JOUR

AU - Donaire, Juan Jesús

AU - Pommerenke, Christian

TI - On radial behaviour and balanced Bloch functions.

JO - Revista Matemática Iberoamericana

PY - 1999

VL - 15

IS - 3

SP - 429

EP - 449

AB - 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 ∈ T or for none.

LA - eng

KW - Funciones analíticas; Aplicación conforme; Bloch functions; conformal mappings

UR - http://eudml.org/doc/39582

ER -

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