Currently displaying 1 – 16 of 16

Showing per page

Order by Relevance | Title | Year of publication

On radial behaviour and balanced Bloch functions.

Juan Jesús DonaireChristian Pommerenke — 1999

Revista Matemática Iberoamericana

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 ...

On the angular limits of Bloch functions.

Joan J. CarmonaJulià CufiChristian Pommerenke — 1988

Publicacions Matemàtiques

This paper contains a method to associate to each function f in the little Bloch space another function f* in the Bloch space in such way that f has a finite angular limit where f* is radially bounded. The idea of the method comes from the theory of lacunary series. An application to conformal mapping from the unit disc to asymptotically Jordan domains is given.

Page 1

Download Results (CSV)