Counterexamples on non-α-normal functions with good integrability

Rauno Aulaskari*, Shamil Makhmutov, Jouni Rättyä

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 Nα when 0 <α< 2.This implies that M#p is in a sense a much larger class than Q#p.

Original languageEnglish
Pages (from-to)165-175
Number of pages11
JournalNew York Journal of Mathematics
Volume17 A
Publication statusPublished - 2011


  • Blaschke product
  • Dirichlet space
  • Normal function

ASJC Scopus subject areas

  • General Mathematics


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