### 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 |

### Fingerprint

### Keywords

- Blaschke product
- Dirichlet space
- Normal function

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*New York Journal of Mathematics*,

*17 A*, 165-175.

**Counterexamples on non-α-normal functions with good integrability.** / Aulaskari, Rauno; Makhmutov, Shamil; Rättyä, Jouni.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - Counterexamples on non-α-normal functions with good integrability

AU - Aulaskari, Rauno

AU - Makhmutov, Shamil

AU - Rättyä, Jouni

PY - 2011

Y1 - 2011

N2 - 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 α when 0 #p is in a sense a much larger class than Q#p.

AB - 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 α when 0 #p is in a sense a much larger class than Q#p.

KW - Blaschke product

KW - Dirichlet space

KW - Normal function

UR - http://www.scopus.com/inward/record.url?scp=80053054709&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053054709&partnerID=8YFLogxK

M3 - Article

VL - 17 A

SP - 165

EP - 175

JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

SN - 1076-9803

ER -