### Abstract

We prove that if G is an analytic function in the unit disc such that G(z) → ∞, as z → 1, and B is an infinite Blaschke product whose sequence of zeros is contained in a Stolz angle with vertex at 1 then the function f = B · G is not a normal function. We prove also some results on the asymptotic cluster set of a thin Blaschke product with positive zeros which are related with the question of the existence of non-normal outer functions with restricted mean growth of the derivative. © Revista Matemática Complutense 2010.

Original language | English |
---|---|

Pages (from-to) | 49-57 |

Journal | Revista Matematica Complutense |

Volume | 24 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2011 |

### Keywords

- Blaschke product
- Bloch function
- Interpolating blaschke sequence
- Mean lipschitz spaces
- Normal function
- Outer function
- Thin blaschke product

## Fingerprint Dive into the research topics of 'On Blaschke products, Bloch functions and normal functions'. Together they form a unique fingerprint.

## Cite this

Girela, D., & Suárez, D. (2011). On Blaschke products, Bloch functions and normal functions.

*Revista Matematica Complutense*,*24*(1), 49-57. https://doi.org/10.1007/s13163-010-0027-6