We prove that, for any finite Blaschke product w=B(z) in the unit disk, the corresponding Riemann surface over the w–plane contains a one-sheeted disk of the radius 0.5. Moreover, it contains a unit one-sheeted disk with a radial slit. We apply this result to obtain a universal lower estimate of the Bloch seminorm for finite Blaschke products.

Original languageEnglish
Article number125983
JournalJournal of Mathematical Analysis and Applications
Volume509
Issue number2
DOIs
StatePublished - 15 May 2022

    Research areas

  • Blaschke product, Bloch seminorm, Bounded analytic function, Riemann surface

    Scopus subject areas

  • Analysis
  • Applied Mathematics

ID: 100818933