On Blaschke products, Bloch functions and normal functions

Daniel Girela, Daniel Suárez

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    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 languageEnglish
    Pages (from-to)49-57
    JournalRevista Matematica Complutense
    Volume24
    Issue number1
    DOIs
    Publication statusPublished - 1 Jan 2011

    Keywords

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

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