### Abstract

Blaschke products are used to construct concrete examples of analytic functions with good integrability and bad behavior of spherical derivative. These examples are used to show that none of the classes M^{#}_{p}, 0 <p <∞, is contained in the α-normal class N^{α} when 0 #_{p} is in a sense a much larger class than Q^{#}_{p}.

Original language | English |
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Pages (from-to) | 165-175 |

Number of pages | 11 |

Journal | New York Journal of Mathematics |

Volume | 17 A |

Publication status | Published - 2011 |

### Keywords

- Blaschke product
- Dirichlet space
- Normal function

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Aulaskari, R., Makhmutov, S., & Rättyä, J. (2011). Counterexamples on non-α-normal functions with good integrability.

*New York Journal of Mathematics*,*17 A*, 165-175.